A326150 - OEIS

%I #6 Jun 10 2019 06:16:21

%S 9,30,49,63,65,81,84,108,125,150,154,165,169,190,198,200,259,264,273,

%T 333,351,361,364,385,390,435,442,468,481,490,495,506,525,561,580,595,

%U 609,624,630,658,675,700,714,741,765,781,783,810,840,841,846,874,900,918

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

%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.

%e The sequence of terms together with their prime indices begins:

%e     9: {2,2}

%e    30: {1,2,3}

%e    49: {4,4}

%e    63: {2,2,4}

%e    65: {3,6}

%e    81: {2,2,2,2}

%e    84: {1,1,2,4}

%e   108: {1,1,2,2,2}

%e   125: {3,3,3}

%e   150: {1,2,3,3}

%e   154: {1,4,5}

%e   165: {2,3,5}

%e   169: {6,6}

%e   190: {1,3,8}

%e   198: {1,2,2,5}

%e   200: {1,1,1,3,3}

%e   259: {4,12}

%e   264: {1,1,1,2,5}

%e   273: {2,4,6}

%e   333: {2,2,12}

%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];

%t Select[Range[2,1000],!PrimeQ[#]&&Divisible[Times@@primeMS[#],Plus@@primeMS[#]]&]

%Y Satisfies A056239(a(n))|A003963(a(n)).

%Y The case with primes included is A326149. The squarefree case A326158.

%Y Cf. A057567, A057568, A112798, A301987.

%Y Cf. A325037, A325042, A325044, A326151, A326153/A326154, A326155, A326156.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jun 09 2019