A064574 Number of partitions of n into parts which are all powers of the same composite.

0, 0, 0, 1, 1, 2, 2, 4, 5, 6, 6, 9, 9, 10, 11, 15, 15, 18, 18, 22, 23, 24, 24, 30, 31, 32, 34, 38, 38, 42, 42, 48, 49, 50, 51, 60, 60, 61, 62, 69, 69, 74, 74, 79, 82, 83, 83, 94, 95, 98, 99, 105, 105, 111, 112, 120, 121, 122, 122, 134, 134, 135, 138, 149, 150, 155, 155

Offset: 1

Author

Marc LeBrun, Sep 20 2001

Keywords

• easy
• nonn

Comments

The exponents cannot all be 0.

Diverges from A028422 at n=20.

Examples

			a(8)=4: 8^1, 6^1+2*6^0, 2*4^1, 4^1+4*2^0
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

A002808, A064572, A064573, A064575, A064576, A064577, A028422.

Programs

PARI

first(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)} \\ Andrew Howroyd, Dec 29 2017

Formula

G.f.: Sum_{k>=1} 1/(Product_{r>=0} 1-x^(A002808(k)^r)) - 1/(1-x). - Andrew Howroyd, Dec 29 2017

Extensions

Name clarified by Andrew Howroyd, Dec 29 2017