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%I #19 Oct 09 2019 10:49:29
%S 1,0,1,1,1,1,3,2,3,4,4,6,8,8,10,13,13,20,20,24,26,38,35,51,51,65,67,
%T 92,86,121,117,153,155,209,197,270,262,339,341,444,425,565,555,703,
%U 711,903,884,1135,1128,1397,1430,1766,1757,2193,2214,2691,2762,3344
%N Number of partitions of n in which each part occurs a prime number (or 0) times.
%H Vaclav Kotesovec, <a href="/A055923/b055923.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Alois P. Heinz)
%F EULER transform of b where b has g.f. Sum {k>0} c(k)*x^k/(1-x^k) where c is inverse EULER transform of characteristic function of prime numbers.
%F G.f.: Product(1+Sum(x^(i*prime(k)), k=1..infinity), i=1..infinity). - _Vladeta Jovovic_, Jan 08 2005
%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p add(`if`(isprime(j), b(n-i*j, i-1), 0), j=1..n/i) +b(n, i-1)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..60); # _Alois P. Heinz_, May 31 2014
%t b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[PrimeQ[j], b[n-i*j, i-1], 0], {j, 1, n/i}] + b[n, i-1]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)
%Y Cf. A000041, A007690, A055922.
%K nonn
%O 0,7
%A _Christian G. Bower_, Jun 23 2000
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