A327901 - OEIS

%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