cp's OEIS Frontend

A327902 Nonprime squarefree numbers whose prime indices all have the same average of prime indices (A326567/A326568).

%I A327902 #6 Oct 01 2019 09:48:57
%S A327902 1,21,57,115,133,145,159,371,393,399,515,535,565,667,803,869,917,933,
%T A327902 1007,1067,1113,1963,2021,2095,2157,2165,2177,2249,2285,2315,2363,
%U A327902 2369,2461,2489,2599,2705,2751,2839,2987,3021,3103,3277,3335,3707,3859,4331,4367
%N A327902 Nonprime squarefree numbers whose prime indices all have the same average of prime indices (A326567/A326568).
%C A327902 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.
%e A327902 The sequence of terms together with their prime indices begins:
%e A327902      1: {}
%e A327902     21: {2,4}
%e A327902     57: {2,8}
%e A327902    115: {3,9}
%e A327902    133: {4,8}
%e A327902    145: {3,10}
%e A327902    159: {2,16}
%e A327902    371: {4,16}
%e A327902    393: {2,32}
%e A327902    399: {2,4,8}
%e A327902    515: {3,27}
%e A327902    535: {3,28}
%e A327902    565: {3,30}
%e A327902    667: {9,10}
%e A327902    803: {5,21}
%e A327902    869: {5,22}
%e A327902    917: {4,32}
%e A327902    933: {2,64}
%e A327902   1007: {8,16}
%e A327902   1067: {5,25}
%t A327902 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A327902 Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Mean/@primeMS/@primeMS[#]&];
%Y A327902 The version including primes and nonsquarefree numbers is A326536.
%Y A327902 The version for number of prime indices is A327900.
%Y A327902 The version for sum of prime indices is A327901.
%Y A327902 Cf. A001222, A005117, A056239, A078175, A102627, A112798, A316413, A326567/A326568, A326621, A327908.
%K A327902 nonn
%O A327902 1,2
%A A327902 _Gus Wiseman_, Sep 30 2019