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

30, 65, 154, 165, 190, 259, 273, 385, 390, 435, 442, 481, 506, 561, 595, 609, 658, 714, 741, 781, 874, 935, 1001, 1110, 1118, 1173, 1254, 1281, 1330, 1363, 1403, 1430, 1455, 1469, 1495, 1505, 1653, 1691, 1771, 1786, 1794, 1798, 1887, 1958, 2035, 2067, 2139

Offset: 1

Author

Gus Wiseman, Jun 10 2019

Keywords

• nonn

Comments

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.

Examples

			The sequence of terms together with their prime indices begins:
    30: {1,2,3}
    65: {3,6}
   154: {1,4,5}
   165: {2,3,5}
   190: {1,3,8}
   259: {4,12}
   273: {2,4,6}
   385: {3,4,5}
   390: {1,2,3,6}
   435: {2,3,10}
   442: {1,6,7}
   481: {6,12}
   506: {1,5,9}
   561: {2,5,7}
   595: {3,4,7}
   609: {2,4,10}
   658: {1,4,15}
   714: {1,2,4,7}
   741: {2,6,8}
   781: {5,20}
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

The case with squarefree numbers included is A326150.

The case with primes and squarefree numbers included is A326149.

Cf. A057567, A057568, A112798, A301987.

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

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[2,1000],!PrimeQ[#]&&SquareFreeQ[#]&&Divisible[Times@@primeMS[#],Plus@@primeMS[#]]&]