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%I #6 Oct 01 2019 09:48:50
%S 1,35,143,209,247,391,493,629,667,851,901,1073,1219,1333,1457,1537,
%T 1891,1961,2021,2201,2623,2717,2759,2867,2993,3053,3239,3337,3827,
%U 3977,4061,4183,4223,4331,4387,4633,5429,5633,5767,5959,6157,6191,6319,7081,7093,7519
%N Nonprime squarefree numbers whose prime indices all have the same sum of prime indices (A056239).
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%H 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 The sequence of terms together with their prime indices begins:
%e 1: {}
%e 35: {3,4}
%e 143: {5,6}
%e 209: {5,8}
%e 247: {6,8}
%e 391: {7,9}
%e 493: {7,10}
%e 629: {7,12}
%e 667: {9,10}
%e 851: {9,12}
%e 901: {7,16}
%e 1073: {10,12}
%e 1219: {9,16}
%e 1333: {11,14}
%e 1457: {11,15}
%e 1537: {10,16}
%e 1891: {11,18}
%e 1961: {12,16}
%e 2021: {14,15}
%e 2201: {11,20}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Total/@primeMS/@primeMS[#]&];
%Y The version including primes and nonsquarefree numbers is A326534.
%Y The version for number of prime indices is A327900.
%Y The version for mean of prime indices is A327902.
%Y Cf. A001222, A005117, A056239, A112798, A302242, A306021, A320324, A326566, A326574, A327908.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 30 2019
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