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A326158 Nonprime squarefree numbers whose product of prime indices is divisible by their sum of prime indices.

%I A326158 #8 Jan 11 2021 02:50:26
%S A326158 30,65,154,165,190,259,273,385,390,435,442,481,506,561,595,609,658,
%T A326158 714,741,781,874,935,1001,1110,1118,1173,1254,1281,1330,1363,1403,
%U A326158 1430,1455,1469,1495,1505,1653,1691,1771,1786,1794,1798,1887,1958,2035,2067,2139
%N A326158 Nonprime squarefree numbers whose product of prime indices is divisible by their sum of prime indices.
%C A326158 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 A326158 Amiram Eldar, <a href="/A326158/b326158.txt">Table of n, a(n) for n = 1..10000</a>
%e A326158 The sequence of terms together with their prime indices begins:
%e A326158     30: {1,2,3}
%e A326158     65: {3,6}
%e A326158    154: {1,4,5}
%e A326158    165: {2,3,5}
%e A326158    190: {1,3,8}
%e A326158    259: {4,12}
%e A326158    273: {2,4,6}
%e A326158    385: {3,4,5}
%e A326158    390: {1,2,3,6}
%e A326158    435: {2,3,10}
%e A326158    442: {1,6,7}
%e A326158    481: {6,12}
%e A326158    506: {1,5,9}
%e A326158    561: {2,5,7}
%e A326158    595: {3,4,7}
%e A326158    609: {2,4,10}
%e A326158    658: {1,4,15}
%e A326158    714: {1,2,4,7}
%e A326158    741: {2,6,8}
%e A326158    781: {5,20}
%t A326158 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A326158 Select[Range[2,1000],!PrimeQ[#]&&SquareFreeQ[#]&&Divisible[Times@@primeMS[#],Plus@@primeMS[#]]&]
%Y A326158 Satisfies A056239(a(n))|A003963(a(n)).
%Y A326158 The case with squarefree numbers included is A326150.
%Y A326158 The case with primes and squarefree numbers included is A326149.
%Y A326158 Cf. A057567, A057568, A112798, A301987.
%Y A326158 Cf. A325037, A325042, A325044, A326151, A326153/A326154, A326155, A326156.
%K A326158 nonn
%O A326158 1,1
%A A326158 _Gus Wiseman_, Jun 10 2019