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A327908 Nonprime squarefree numbers whose prime indices all have the same Omega (A001222) and the same sum of prime indices (A056239).

%I A327908 #6 Oct 01 2019 09:50:26
%S A327908 1,667,2021,4331,5767,7081,7663,11021,11639,12091,13837,15049,20413,
%T A327908 23213,26123,31553,34933,35657,35723,37909,37979,38021,41449,42919,
%U A327908 44197,45113,51019,53531,58339,63407,66013,70531,72929,73373,73903,75763,83411,87361,90581
%N A327908 Nonprime squarefree numbers whose prime indices all have the same Omega (A001222) and the same sum of prime indices (A056239).
%H A327908 Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%e A327908 The sequence of terms together with their prime indices begins:
%e A327908       1: {}
%e A327908     667: {9,10}
%e A327908    2021: {14,15}
%e A327908    4331: {18,20}
%e A327908    5767: {21,22}
%e A327908    7081: {21,25}
%e A327908    7663: {22,25}
%e A327908   11021: {27,28}
%e A327908   11639: {27,30}
%e A327908   12091: {28,30}
%e A327908   13837: {26,33}
%e A327908   15049: {26,35}
%e A327908   20413: {33,35}
%e A327908   23213: {34,39}
%e A327908   26123: {36,40}
%e A327908   31553: {34,49}
%e A327908   34933: {42,44}
%e A327908   35657: {42,45}
%e A327908   35723: {34,55}
%e A327908   37909: {39,49}
%t A327908 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327908 Select[Range[10000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@primeMS[#]&&SameQ@@Total/@primeMS/@primeMS[#]&]
%Y A327908 Equal omega: A327900
%Y A327908 Equal sum of prime indices: A327901
%Y A327908 Equal average of prime indices: A327902
%Y A327908 Cf. A001222, A038041, A056239, A112798, A320324, A326574, A327899.
%K A327908 nonn
%O A327908 1,2
%A A327908 _Gus Wiseman_, Sep 30 2019