Sequences

Number of partitions of n into parts not of the form 25k, 25k+12 or 25k-12. Also number of partitions with at most 11 parts of size 1 and differences between parts at distance 11 are greater than 1.

a(n) = smallest number > 1 such that a(1)a(2)...a(n) + 1 is prime.

a(n) = smallest number > 1 such that a(1)a(2)...a(n) - 1 is prime (or 1).

a(n) is the smallest number such that the product a(1)a(2)...a(n) falls between a twin prime pair, starting with a(1)=2.

Number of partitions of n into parts not of form 4k+2, 8k, 8k+1 or 8k-1.

Number of partitions of n into parts not of form 4k+2, 8k, 8k+3 or 8k-3.

Number of partitions of n into parts not of form 4k+2, 12k, 12k+1 or 12k-1.

Number of partitions of n into parts not of form 4k+2, 12k, 12k+3 or 12k-3.

Number of partitions of n into parts not of form 4k+2, 12k, 12k+5 or 12k-5.

Number of partitions of n into parts not of form 4k+2, 16k, 16k+1 or 16k-1.

Number of partitions of n into parts not of form 4k+2, 16k, 16k+3 or 16k-3.

Number of partitions of n into parts not of form 4k+2, 16k, 16k+5 or 16k-5.

Number of partitions of n into parts not of form 4k+2, 16k, 16k+7 or 16k-7.

Number of partitions of n into parts not of form 4k+2, 20k, 20k+1 or 20k-1. Also number of partitions in which no odd part is repeated, with no part of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 20k, 20k+3 or 20k-3. Also number of partitions in which no odd part is repeated, with 1 part of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of forms 4*k+2, 20*k, 10*k+5.

Number of partitions of n into parts not of form 4k+2, 20k, 20k+7 or 20k-7. Also number of partitions in which no odd part is repeated, with at most 3 parts of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 20k, 20k+9 or 20k-9. Also number of partitions in which no odd part is repeated, with at most 4 parts of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 24k, 24k+1 or 24k-1. Also number of partitions in which no odd part is repeated, with no part of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 24k, 24k+3 or 24k-3. Also number of partitions in which no odd part is repeated, with 1 part of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 24k, 24k+5 or 24k-5. Also number of partitions in which no odd part is repeated, with at most 2 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 24k, 24k+7 or 24k-7. Also number of partitions in which no odd part is repeated, with at most 3 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 24k, 24k+9 or 24k-9. Also number of partitions in which no odd part is repeated, with at most 4 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Number of partitions of n into parts not of form 4k+2, 24k, 24k+11 or 24k-11. Also number of partitions in which no odd part is repeated, with at most 5 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

Least integer of each prime signature, in graded (reflected or not) colexicographic order of exponents.

Triangle read by rows in which row n lists all the parts of all reversed partitions of n, sorted first by length and then lexicographically.

Triangle read by rows in which row n lists all the parts of all the partitions of n, sorted first by length and then colexicographically.

Triangle T(n,k) read by rows: multinomial coefficients for the partitions of n listed in Abramowitz-Stegun order, 1 <= k <= A000041(n).

Irregular triangle of multinomial coefficients of integer partitions read by rows (in Abramowitz and Stegun ordering) giving the coefficients of the cycle index polynomials for the symmetric groups S_n.

Irregular triangle of multinomial coefficients, read by rows (version 1).

Number of prime divisors, counted with multiplicity, of prime signature A025487(n); equals size of associated partition.

k appears partition(k) times.

Irregular triangle read by rows: row n (n >= 0) gives number of parts in all partitions of n (in Abramowitz and Stegun order).

BCR(n): write in binary, complement, reverse.

Sum of distances between dual pairs of partitions of n for the canonical order.

Product of the lengths of the cycle types of the permutation created by duality and reversal on the partitions of n.

Product of order of cycles of the permutation created by duality and reversal on the partitions of n.

Number of different cycle lengths of the permutation created by duality and reversal on the partitions of n.

Number of cycles of the permutation created by duality and reversal on the partitions of n.

Sum of the lengths of the cycle types of the permutation created by duality and reversal on the partitions of n.

Sum of distances between greatest-part-order and length-order of partitions of n.

Product of the lengths of the cycle types of the permutation created by length sorting on the partitions of n.

Product of order of cycles of the permutation created by length sorting on the partitions of n.

Number of different cycle lengths of the permutation created by length sorting on the partitions of n.

Number of cycles of the permutation created by length sorting on the partitions of n.

Sum of the lengths of the cycle types of the permutation created by length sorting on the partitions of n.

Friedman numbers: can be written in a nontrivial way using their digits and the operations + - * / ^ and concatenation of digits (but not of results).

Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.

The summarize Fibonacci sequence: summarize the previous two terms!.

Number of 3-component Carmichael numbers C = (6M + 1)(12M + 1)(18M + 1) < 10^n.