Sequences

First differences of A037260.

Second differences of A037260.

Third differences of A037260.

Numbers whose sum of reciprocals of digits is the reciprocal of an integer.

Integers arising from A037264.

Numbers k such that no extremal Groemer packing of k circles exists.

Number of Boolean functions on n inputs with representing polynomial of max degree n.

Sum of reciprocals of digits = 1.

Expansion of (1+x^30)/((1-x^4)(1-x^5)(1-x^6)(1-x^12)).

a(n) = n^2*(n^2 + 1)/2.

Number of steps to reach a prime under "replace n with concatenation of its prime factors" when applied to n-th composite number, or -1 if no such number exists.

Primes reached in A037271, or -1 if no such prime exists.

Number of steps to reach a prime under "replace n with concatenation of its prime factors", or -1 if no prime is ever reached.

Home primes: for n >= 2, a(n) = the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached (a(n) = -1 if no prime is ever reached).

Subsequence of record holders in A037274.

Start with 1; for n>1, replace n with the concatenation of its prime factors in increasing order.

Replace n with concatenation of its divisors >1.

Replace n with concatenation of its divisors.

If n is composite, replace n with the concatenation of its nontrivial divisors, otherwise a(n) = n.

If n is composite replace n with the concatenation of its nontrivial divisors [ A037279 ] then divide out any factors of 2.

Number of iterations of transformation in A037280 needed to reach 1 or a prime, or -1 if no such number exists.

Scan n from left to right once, erasing any primes.

Replace n with concatenation of its odd divisors.

Replace n with concatenation of its odd divisors >1.

Replace n with concatenation of its nontrivial odd divisors.

Replace 2n+1 with concatenation of its divisors.

Replace 2n+1 with concatenation of its divisors >1.

Replace 2n+1 with concatenation of its nontrivial divisors.

Number of commutative rings with n elements.

Number of self-converse rings (isomorphic to inverse) with n elements.

Number of rings with 1 containing n elements.

Number of nonassociative rings with n elements.

a(n) = Sum_{i=0..2^(n-1)} binomial(2^(n-1), i)^2.

Number of (s,2) gates.

Number of (s,3) gates.

Number of (s,4) gates.

Number of (s,5) gates.

Number of (s,6) gates.

Prime substrings of prime numbers in A037272.

Number of prime substrings of prime numbers in A037272.

Numbers whose base-2 and base-3 expansions have the same digit sum.

Normalized volume of Birkhoff polytope of n X n doubly-stochastic square matrices. If the volume is v(n), then a(n) = ((n-1)^2)! * v(n) / n^(n-1).

Numbers whose base-2 and base-5 expansions have the same digit sum.

Numbers whose base-2 and base-6 expansions have the same digit sum.

Numbers whose base-2 and base-7 expansions have the same digit sum.

Triangle T(n,k) read by rows: the number of compositions of n into k parts, modulo cyclic shifts.

Numbers whose base-2 and base-9 expansions have the same digit sum.

Numbers whose base-2 and base-10 expansions have the same digit sum.

Numbers whose base-3 and base-4 expansions have the same digit sum.

Numbers whose base-3 and base-5 expansions have the same digit sum.