A213016 Numbers n such that the sum of prime factors of n (counted with multiplicity) is 3 times a prime.

8, 9, 14, 20, 24, 26, 27, 38, 44, 62, 68, 74, 105, 112, 116, 125, 126, 134, 150, 160, 180, 188, 192, 195, 208, 212, 216, 218, 231, 234, 243, 254, 275, 278, 314, 330, 332, 343, 352, 356, 362, 396, 398, 422, 428, 465, 483, 490, 496, 548, 558, 575, 588, 609, 614

Offset: 1

Author

Michel Lagneau, Jun 02 2012

Keywords

• nonn

Comments

The numbers A100118(n)^3 are in the sequence.

Examples

			44 is in the sequence because 44 = 2^2 * 11 => sum of prime factors = 2*2+11 = 15 = 3*5 where 5 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001414, A100118, A213015.

Programs

Maple

with(numtheory):A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end: for m from 1 to 3000 do: if type(A(m)/3,prime)= true then printf(`%d, `,m):else fi:od:

Mathematica

L = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[PrimeQ[w/3], AppendTo[L, k]], {k, 2, 1000}]; L
Select[Range[700],PrimeQ[Total[Times@@@FactorInteger[#]]/3]&] (* Harvey P. Dale, Nov 23 2022 *)

Formula

sopfr(n) = 3*p, p prime.