cp's OEIS Frontend

A326150 Nonprime numbers whose product of prime indices is divisible by their sum of prime indices.

%I A326150 #6 Jun 10 2019 06:16:21
%S A326150 9,30,49,63,65,81,84,108,125,150,154,165,169,190,198,200,259,264,273,
%T A326150 333,351,361,364,385,390,435,442,468,481,490,495,506,525,561,580,595,
%U A326150 609,624,630,658,675,700,714,741,765,781,783,810,840,841,846,874,900,918
%N A326150 Nonprime numbers whose product of prime indices is divisible by their sum of prime indices.
%C A326150 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 A326150 The sequence of terms together with their prime indices begins:
%e A326150     9: {2,2}
%e A326150    30: {1,2,3}
%e A326150    49: {4,4}
%e A326150    63: {2,2,4}
%e A326150    65: {3,6}
%e A326150    81: {2,2,2,2}
%e A326150    84: {1,1,2,4}
%e A326150   108: {1,1,2,2,2}
%e A326150   125: {3,3,3}
%e A326150   150: {1,2,3,3}
%e A326150   154: {1,4,5}
%e A326150   165: {2,3,5}
%e A326150   169: {6,6}
%e A326150   190: {1,3,8}
%e A326150   198: {1,2,2,5}
%e A326150   200: {1,1,1,3,3}
%e A326150   259: {4,12}
%e A326150   264: {1,1,1,2,5}
%e A326150   273: {2,4,6}
%e A326150   333: {2,2,12}
%t A326150 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A326150 Select[Range[2,1000],!PrimeQ[#]&&Divisible[Times@@primeMS[#],Plus@@primeMS[#]]&]
%Y A326150 Satisfies A056239(a(n))|A003963(a(n)).
%Y A326150 The case with primes included is A326149. The squarefree case A326158.
%Y A326150 Cf. A057567, A057568, A112798, A301987.
%Y A326150 Cf. A325037, A325042, A325044, A326151, A326153/A326154, A326155, A326156.
%K A326150 nonn
%O A326150 1,1
%A A326150 _Gus Wiseman_, Jun 09 2019