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%I #5 May 08 2019 22:20:04
%S 1,2,3,5,6,7,10,11,13,14,15,17,19,21,22,23,24,26,29,31,33,34,35,37,38,
%T 39,40,41,43,46,47,51,53,54,55,56,57,58,59,61,62,65,67,69,71,73,74,77,
%U 79,82,83,85,86,87,88,89,91,93,94,95,97,101,103,104,106
%N Numbers whose prime signature is that of a factorial number.
%C A181819(a(n)) belongs to A325508.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 3: {2}
%e 5: {3}
%e 6: {1,2}
%e 7: {4}
%e 10: {1,3}
%e 11: {5}
%e 13: {6}
%e 14: {1,4}
%e 15: {2,3}
%e 17: {7}
%e 19: {8}
%e 21: {2,4}
%e 22: {1,5}
%e 23: {9}
%e 24: {1,1,1,2}
%e 26: {1,6}
%e 29: {10}
%e 31: {11}
%t Select[Range[30],MemberQ[Table[Sort[Last/@FactorInteger[k!]],{k,#}],Sort[Last/@FactorInteger[#]]]&]
%Y Cf. A000142, A011371, A022559, A076934, A115627, A181819, A325272, A325276, A325508, A325509, A325510.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 08 2019