A303663 Expansion of (1/(1 - x))*Product_{k>=1} (1 - x^prime(k))/(1 - x^k).

1, 2, 3, 4, 6, 8, 11, 14, 19, 25, 33, 41, 53, 66, 83, 102, 128, 156, 193, 233, 285, 343, 416, 495, 597, 710, 849, 1003, 1194, 1404, 1662, 1946, 2291, 2675, 3137, 3646, 4260, 4939, 5744, 6637, 7697, 8868, 10250, 11778, 13570, 15558, 17877, 20437, 23423, 26727, 30550, 34781, 39669, 45068, 51287, 58157

Offset: 0

Author

Ilya Gutkovskiy, Apr 28 2018

Keywords

• nonn
• easy

Comments

Partial sums of A002095.

Number of partitions of n into nonprime parts if there are two kinds of 1's.

Links

• David A. Corneth, Table of n, a(n) for n = 0..9999
• Index entries for sequences related to partitions

Crossrefs

Cf. A000070, A002095, A018252, A023895, A034891.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0 or i=1, n+1,
      b(n, i-1)+`if`(isprime(i), 0, b(n-i, min(n-i, i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..60);  # Alois P. Heinz, Apr 28 2018

Mathematica

nmax = 55; CoefficientList[Series[1/(1 - x) Product[(1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]