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

%I A303663 #11 Sep 06 2020 06:41:19
%S A303663 1,2,3,4,6,8,11,14,19,25,33,41,53,66,83,102,128,156,193,233,285,343,
%T A303663 416,495,597,710,849,1003,1194,1404,1662,1946,2291,2675,3137,3646,
%U A303663 4260,4939,5744,6637,7697,8868,10250,11778,13570,15558,17877,20437,23423,26727,30550,34781,39669,45068,51287,58157
%N A303663 Expansion of (1/(1 - x))*Product_{k>=1} (1 - x^prime(k))/(1 - x^k).
%C A303663 Partial sums of A002095.
%C A303663 Number of partitions of n into nonprime parts if there are two kinds of 1's.
%H A303663 David A. Corneth, <a href="/A303663/b303663.txt">Table of n, a(n) for n = 0..9999</a>
%H A303663 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%p A303663 b:= proc(n, i) option remember; `if`(n=0 or i=1, n+1,
%p A303663       b(n, i-1)+`if`(isprime(i), 0, b(n-i, min(n-i, i))))
%p A303663     end:
%p A303663 a:= n-> b(n$2):
%p A303663 seq(a(n), n=0..60);  # _Alois P. Heinz_, Apr 28 2018
%t A303663 nmax = 55; CoefficientList[Series[1/(1 - x) Product[(1 - x^Prime[k])/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A303663 Cf. A000070, A002095, A018252, A023895, A034891.
%K A303663 nonn,easy
%O A303663 0,2
%A A303663 _Ilya Gutkovskiy_, Apr 28 2018