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

9, 30, 49, 63, 65, 81, 84, 108, 125, 150, 154, 165, 169, 190, 198, 200, 259, 264, 273, 333, 351, 361, 364, 385, 390, 435, 442, 468, 481, 490, 495, 506, 525, 561, 580, 595, 609, 624, 630, 658, 675, 700, 714, 741, 765, 781, 783, 810, 840, 841, 846, 874, 900, 918

Offset: 1

Author

Gus Wiseman, Jun 09 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:
    9: {2,2}
   30: {1,2,3}
   49: {4,4}
   63: {2,2,4}
   65: {3,6}
   81: {2,2,2,2}
   84: {1,1,2,4}
  108: {1,1,2,2,2}
  125: {3,3,3}
  150: {1,2,3,3}
  154: {1,4,5}
  165: {2,3,5}
  169: {6,6}
  190: {1,3,8}
  198: {1,2,2,5}
  200: {1,1,1,3,3}
  259: {4,12}
  264: {1,1,1,2,5}
  273: {2,4,6}
  333: {2,2,12}
		

Crossrefs

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

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

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[#]&&Divisible[Times@@primeMS[#],Plus@@primeMS[#]]&]