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%I #4 May 03 2019 21:25:43
%S 1,6,21,30,65,133,210,273,319,481,731,1007,1403,1495,2059,2310,2449,
%T 3293,4141,4601,4921,5187,5311,6943,8201,9211,10921,12283,13213,14993,
%U 15247,16517,19847,22213,24139,25853,28141,29341,29539,30030,31753,37211,40741
%N Nonprime Heinz numbers of multiples of triangular partitions, or of finite arithmetic progressions with offset 0.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers of the form Product_{k = 1...b} prime(k * c) for some b > 1 and c > 0.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 6: {1,2}
%e 21: {2,4}
%e 30: {1,2,3}
%e 65: {3,6}
%e 133: {4,8}
%e 210: {1,2,3,4}
%e 273: {2,4,6}
%e 319: {5,10}
%e 481: {6,12}
%e 731: {7,14}
%e 1007: {8,16}
%e 1403: {9,18}
%e 1495: {3,6,9}
%e 2059: {10,20}
%e 2310: {1,2,3,4,5}
%e 2449: {11,22}
%e 3293: {12,24}
%e 4141: {13,26}
%e 4601: {14,28}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[10000],!PrimeQ[#]&&SameQ@@Differences[Prepend[primeMS[#],0]]&]
%Y Cf. A007294, A007862, A049988, A056239, A112798, A325327, A325328, A325355, A325359, A325367, A325390.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 03 2019
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