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A325407 Nonprime Heinz numbers of multiples of triangular partitions, or of finite arithmetic progressions with offset 0.

%I A325407 #4 May 03 2019 21:25:43
%S A325407 1,6,21,30,65,133,210,273,319,481,731,1007,1403,1495,2059,2310,2449,
%T A325407 3293,4141,4601,4921,5187,5311,6943,8201,9211,10921,12283,13213,14993,
%U A325407 15247,16517,19847,22213,24139,25853,28141,29341,29539,30030,31753,37211,40741
%N A325407 Nonprime Heinz numbers of multiples of triangular partitions, or of finite arithmetic progressions with offset 0.
%C A325407 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 A325407 The sequence of terms together with their prime indices begins:
%e A325407       1: {}
%e A325407       6: {1,2}
%e A325407      21: {2,4}
%e A325407      30: {1,2,3}
%e A325407      65: {3,6}
%e A325407     133: {4,8}
%e A325407     210: {1,2,3,4}
%e A325407     273: {2,4,6}
%e A325407     319: {5,10}
%e A325407     481: {6,12}
%e A325407     731: {7,14}
%e A325407    1007: {8,16}
%e A325407    1403: {9,18}
%e A325407    1495: {3,6,9}
%e A325407    2059: {10,20}
%e A325407    2310: {1,2,3,4,5}
%e A325407    2449: {11,22}
%e A325407    3293: {12,24}
%e A325407    4141: {13,26}
%e A325407    4601: {14,28}
%t A325407 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325407 Select[Range[10000],!PrimeQ[#]&&SameQ@@Differences[Prepend[primeMS[#],0]]&]
%Y A325407 Cf. A007294, A007862, A049988, A056239, A112798, A325327, A325328, A325355, A325359, A325367, A325390.
%K A325407 nonn
%O A325407 1,2
%A A325407 _Gus Wiseman_, May 03 2019