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

1,1

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.

Links

Table of n, a(n) for n=1..54.

Example

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}

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[#]]&]

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.

Sequence in context: A158503 A179506 A185653 * A167154 A063150 A063161

Adjacent sequences: A326147 A326148 A326149 * A326151 A326152 A326153

Keyword

nonn

Author

Gus Wiseman, Jun 09 2019

Status

approved