cp's OEIS Frontend

A355158 Number of partitions of n that contain more nonprime parts than prime parts.

%I A355158 #38 Jun 30 2022 14:42:49
%S A355158 0,1,1,1,3,4,5,8,12,16,24,29,42,57,74,97,132,165,217,279,355,453,576,
%T A355158 717,908,1135,1408,1751,2169,2664,3283,4022,4909,5990,7282,8814,10681,
%U A355158 12885,15506,18643,22362,26739,31970,38100,45340,53878,63908,75639,89476,105580,124445
%N A355158 Number of partitions of n that contain more nonprime parts than prime parts.
%H A355158 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A355158 a(n) = A000041(n) - A155515(n) - A355225(n).
%F A355158 a(n) = A355306(n) - A355225(n).
%e A355158 For n = 8 the partitions of 8 that contain more nonprime parts than prime parts are [8], [4, 4], [4, 3, 1], [6, 1, 1], [4, 2, 1, 1], [5, 1, 1, 1], [3, 2, 1, 1, 1], [4, 1, 1, 1, 1], [2, 2, 1, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1]. There are 12 of these partitions so a(8) = 12.
%o A355158 (PARI) a(n) = my(nb=0); forpart(p=n, if (#select(x->!isprime(x), Vec(p)) > #p/2, nb++)); nb; \\ _Michel Marcus_, Jun 25 2022
%o A355158 (Python)
%o A355158 from sympy import isprime
%o A355158 from sympy.utilities.iterables import partitions
%o A355158 def c(p): return 2*sum(p[i] for i in p if not isprime(i)) > sum(p.values())
%o A355158 def a(n): return sum(1 for p in partitions(n) if c(p))
%o A355158 print([a(n) for n in range(51)]) # _Michael S. Branicky_, Jun 28 2022
%Y A355158 Cf. A000040, A000041, A000607, A002095, A002096, A018252, A155515, A355225, A355306.
%K A355158 nonn
%O A355158 0,5
%A A355158 _Omar E. Pol_, Jun 24 2022
%E A355158 More terms from _Michel Marcus_, Jun 25 2022