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 A322547 #8 Jul 17 2021 07:00:50
%S A322547 1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,17,19,21,22,23,25,26,27,29,31,33,
%T A322547 34,35,37,39,41,43,47,49,51,53,55,59,61,67,71,79
%N A322547 Numbers k such that every integer partition of k contains a 1, a squarefree number, or a prime power.
%e A322547 48 does not belong to the sequence because there are integer partitions of 48 containing no 1's, squarefree numbers, or prime powers, namely: (48), (36,12), (28,20), (24,24), (24,12,12), (18,18,12), (12,12,12,12).
%t A322547 nn=100;
%t A322547 ser=Product[If[PrimePowerQ[n]||SquareFreeQ[n],1,1/(1-x^n)],{n,nn}];
%t A322547 Join@@Position[CoefficientList[Series[ser,{x,0,nn}],x],0]-1
%Y A322547 Cf. A000607, A002095, A005117, A023893, A023894, A064573, A078135, A101417, A246655, A322546.
%K A322547 nonn,fini,full
%O A322547 1,2
%A A322547 _Gus Wiseman_, Dec 14 2018