A064575 First differences of A064572, where A064572(n) is the number of ways to partition n into parts which are all powers of some integer.

1, 1, 3, 1, 4, 1, 6, 3, 6, 1, 11, 1, 8, 4, 14, 1, 16, 1, 19, 5, 16, 1, 29, 3, 22, 7, 31, 1, 37, 1, 42, 7, 38, 4, 62, 1, 48, 9, 69, 1, 73, 1, 80, 14, 76, 1, 114, 3, 100, 11, 121, 1, 132, 5, 150, 14, 142, 1, 193, 1, 168, 20, 213, 5, 223, 1, 247, 17, 247, 1, 319, 1, 286, 25, 339, 4, 355

Offset: 1

Author

Marc LeBrun, Sep 20 2001

Keywords

• easy
• nonn

Comments

Apparently a(n)=1 when n+1 is prime.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A064572, A064573, A064574, A064576, A064577, A028422.

Programs

PARI

up_to = 200;
A064572list(n) = {Vec(sum(k=2, n, 1/prod(r=0, logint(n, k), 1-x^(k^r) + O(x*x^n)) - 1/(1-x), 0), -n)}; \\ From A064572 by Andrew Howroyd, Dec 29 2017
v064572 = A064572list(1+up_to);
A064572(n) = v064572[n];
A064575(n) = (A064572(1+n)-A064572(n)); \\ Antti Karttunen, Jan 24 2025