OFFSET
1,6
FORMULA
G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(k*(3*k-1)/2) * (1-x^k) * Sum_{p prime} x^(k*p).
EXAMPLE
a(6) = 3 counts these partitions: 6, 5+1, 4+2.
MAPLE
b:= proc(n, i, c) option remember; `if`(i>n, 0, `if`(i=n,
`if`(isprime(i-c, 7), 1, 0), b(n-i, i, c+1)+b(n, i+1, c)))
end:
a:= n-> b(n, 1$2):
seq(a(n), n=1..56); # Alois P. Heinz, May 23 2023
PROG
(PARI) my(N=60, x='x+O('x^N)); concat([0, 0], Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(k*(3*k-1)/2)*(1-x^k)*sum(j=1, N, isprime(j)*x^(k*j)))))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, May 23 2023
STATUS
approved