%I #32 Jun 30 2022 10:38:00
%S 0,0,1,1,1,3,3,5,7,9,14,19,23,34,46,56,77,99,126,164,208,260,336,416,
%T 520,654,809,995,1237,1514,1856,2274,2761,3354,4078,4918,5931,7153,
%U 8572,10272,12298,14663,17469,20787,24643,29210,34568,40797,48113,56664,66573
%N Number of partitions of n that contain more prime parts than nonprime parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = A000041(n) - A155515(n) - A355158(n).
%F a(n) = A355306(n) - A355158(n).
%e For n = 8 the partitions of 8 that contain more prime parts than nonprime parts are [5, 3], [3, 3, 2], [4, 2, 2], [2, 2, 2, 2], [5, 2, 1], [3, 2, 2, 1], [2, 2, 2, 1, 1]. There are seven of these partitions so a(8) = 7.
%o (PARI) a(n) = my(nb=0); forpart(p=n, if (#select(isprime, Vec(p)) > #p/2, nb++)); nb; \\ _Michel Marcus_, Jun 25 2022
%o (Python)
%o from sympy import isprime
%o from sympy.utilities.iterables import partitions
%o def c(p): return 2*sum(p[i] for i in p if isprime(i)) > sum(p.values())
%o def a(n): return sum(1 for p in partitions(n) if c(p))
%o print([a(n) for n in range(51)]) # _Michael S. Branicky_, Jun 28 2022
%Y Cf. A000040, A000041, A000607, A002095, A002096, A018252, A155515, A235945, A355158, A355306.
%K nonn
%O 0,6
%A _Omar E. Pol_, Jun 24 2022
%E More terms from _Alois P. Heinz_, Jun 24 2022