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A327901 Nonprime squarefree numbers whose prime indices all have the same sum of prime indices (A056239).

%I A327901 #6 Oct 01 2019 09:48:50
%S A327901 1,35,143,209,247,391,493,629,667,851,901,1073,1219,1333,1457,1537,
%T A327901 1891,1961,2021,2201,2623,2717,2759,2867,2993,3053,3239,3337,3827,
%U A327901 3977,4061,4183,4223,4331,4387,4633,5429,5633,5767,5959,6157,6191,6319,7081,7093,7519
%N A327901 Nonprime squarefree numbers whose prime indices all have the same sum of prime indices (A056239).
%C A327901 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 A327901 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 A327901 The sequence of terms together with their prime indices begins:
%e A327901      1: {}
%e A327901     35: {3,4}
%e A327901    143: {5,6}
%e A327901    209: {5,8}
%e A327901    247: {6,8}
%e A327901    391: {7,9}
%e A327901    493: {7,10}
%e A327901    629: {7,12}
%e A327901    667: {9,10}
%e A327901    851: {9,12}
%e A327901    901: {7,16}
%e A327901   1073: {10,12}
%e A327901   1219: {9,16}
%e A327901   1333: {11,14}
%e A327901   1457: {11,15}
%e A327901   1537: {10,16}
%e A327901   1891: {11,18}
%e A327901   1961: {12,16}
%e A327901   2021: {14,15}
%e A327901   2201: {11,20}
%t A327901 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327901 Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Total/@primeMS/@primeMS[#]&];
%Y A327901 The version including primes and nonsquarefree numbers is A326534.
%Y A327901 The version for number of prime indices is A327900.
%Y A327901 The version for mean of prime indices is A327902.
%Y A327901 Cf. A001222, A005117, A056239, A112798, A302242, A306021, A320324, A326566, A326574, A327908.
%K A327901 nonn
%O A327901 1,2
%A A327901 _Gus Wiseman_, Sep 30 2019