This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A353188 #22 Jun 23 2022 13:45:51 %S A353188 0,0,0,0,1,1,3,4,8,12,19,27,41,56,80,109,150,199,268,350,461,596,771, %T A353188 984,1258,1589,2007,2514,3145,3905,4846,5973,7356,9010,11020,13418, %U A353188 16315,19756,23890,28788,34639,41548,49767,59441,70899,84354,100221,118803,140645,166153,196035,230853,271512 %N A353188 Number of partitions of n that contain at least one composite part. %F A353188 a(n) = A000041(n) - A034891(n). %e A353188 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 A353188 (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 A353188 Cf. A000041, A002096, A002808, A023895, A034891, A047967, A085642, A086543, A116449, A144300, A204389. %K A353188 nonn %O A353188 0,7 %A A353188 _Omar E. Pol_, Jun 22 2022