Sequences

Number of partitions of n into 8 positive cubes.

Number of partitions of n into 9 positive cubes.

Number of partitions of n into 10 positive cubes.

Number of partitions of n into 2 distinct nonnegative cubes.

Number of partitions of n into 3 distinct nonnegative cubes.

Number of partitions of n into 4 distinct nonnegative cubes.

Expansion of 1/((1-2x)(1-3x)(1-4x)(1-8x)).

a(n) is the number of partitions of n into 2 distinct positive cubes.

Number of partitions of n into 3 distinct positive cubes.

Expansion of 1/((1-2x)(1-3x)(1-4x)(1-9x)).

Position of 5^n among the powers of primes (A000961).

a(n) is the position of 7^n among the powers of primes (A000961).

a(1) = 1; for n > 1, a(n) = prime root of n-th prime power (A000961).

Exponent of the n-th prime power A000961(n).

1 and the prime powers p^m where m >= 2, thus excluding the primes.

Prime root of n-th nontrivial prime power (A025475, A246547).

a(n) = exponent of the n-th nontrivial prime power A025475(n).

Least roots of perfect powers (A001597).

Largest exponents of perfect powers (A001597).

a(2n) = n, a(2n+1) = a(n).

a(0) = 0; a(n) = a(n/2)/2 if n = a(n/2) = 0 (mod 2); a(n) = a(n-1)+1 otherwise.

a(0) = 0; a(n) = a(n/3)/3 if n = a(n/3) = 0 (mod 3); a(n) = a(n-1)+1 otherwise.

a(0) = 0; a(n) = a(n/4)/4 if n = a(n/4) = 0 (mod 4); a(n) = a(n-1)+1 otherwise.

a(0) = 0; a(n) = a(n/5)/5 if n = a(n/5) = 0 (mod 5); a(n) = a(n-1)+1 otherwise.

Number of iterations of function f(k) = ceiling(sqrt(k))^2 - k on n required to force n <= 2.

Least k with A025485(k) = n.

Least integer of each prime signature A124832; also products of primorial numbers A002110.

Number of distinct prime signatures of the positive integers up to 2^n.

Numbers on backgammon doubling cube.

Numbers k such that the sum of the digits of Fibonacci(k) in base 11 is k.

In base 11, a(n) = sum of digits of Lucas(a(n)).

Fixed point reached by iterating the Kempner function A002034 starting at n.

Smallest k that converges after exactly n iterations of the Kempner function A002034.

Squares which are the sum of factorials of distinct integers (probably finite).

Probable extension of A013704.

Number of terms in Zeckendorf representation of 4^n.

Number of terms in Zeckendorf representation of 5^n.

Number of terms in Zeckendorf representation of 6^n.

Number of terms in Zeckendorf representation of 7^n.

Number of terms in Zeckendorf representation of 8^n.

Number of terms in Zeckendorf representation of 9^n.

Number of terms in Zeckendorf representation of 10^n.

Least k such that the first k terms of the Kolakoski sequence (A000002) contain n more 2's than 1's.

Least k>1 such that reverse complement of first n terms of Kolakoski sequence (A000002) repeats beginning at k-th term.

Index of n-th 2 in A006928.

Least k such that first k terms of A006928 contain n more 1's than 2's.

Least k such that the first k terms of A006928 contain n more 2's than 1's.

Least k>1 such that first n terms of A006928 repeat beginning at k-th term.

Least k>1 such that reverse of first n terms of A006928 repeats beginning at k-th term.

Least k>1 such that complement of first n terms of A006928 repeats beginning at k-th term.