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%I #22 Jun 23 2022 13:45:51
%S 0,0,0,0,1,1,3,4,8,12,19,27,41,56,80,109,150,199,268,350,461,596,771,
%T 984,1258,1589,2007,2514,3145,3905,4846,5973,7356,9010,11020,13418,
%U 16315,19756,23890,28788,34639,41548,49767,59441,70899,84354,100221,118803,140645,166153,196035,230853,271512
%N Number of partitions of n that contain at least one composite part.
%F a(n) = A000041(n) - A034891(n).
%e For n = 6 the partitions of 6 that contain at least one composite parts are [6], [4, 2] and [4, 1, 1]. There are three of these partitions so a(6) = 3.
%o (PARI) a(n) = my(nb=0); forpart(p=n, if (#select(x->((x>1) && !isprime(x)), Vec(p)) >=1, nb++);); nb; \\ _Michel Marcus_, Jun 23 2022
%Y Cf. A000041, A002096, A002808, A023895, A034891, A047967, A085642, A086543, A116449, A144300, A204389.
%K nonn
%O 0,7
%A _Omar E. Pol_, Jun 22 2022