A064576 First differences of A064573, where A064573(n) is the number of partitions of n into parts which are all powers of the same prime.

1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 8, 1, 7, 3, 10, 1, 13, 1, 15, 4, 15, 1, 23, 2, 21, 5, 27, 1, 33, 1, 36, 6, 37, 3, 53, 1, 47, 8, 62, 1, 68, 1, 75, 11, 75, 1, 103, 2, 97, 10, 115, 1, 126, 4, 142, 13, 141, 1, 181, 1, 167, 17, 202, 4, 218, 1, 239, 16, 243, 1, 302, 1, 285, 22, 331, 3, 349

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, A064575, A064577, A028422.

Programs

PARI

up_to = 200;
A064573list(n)={Vec(sum(k=2, n, if(isprime(k), 1/prod(r=0, logint(n, k), 1-x^(k^r) + O(x*x^n)) - 1/(1-x), 0)), -n)}; \\ From A064573 by Andrew Howroyd, Dec 29 2017
v064573 = A064573list(1+up_to);
A064573(n) = v064573[n];
A064576(n) = (A064573(1+n)-A064573(n)); \\ Antti Karttunen, Jan 24 2025