A213015 Numbers n such that the sum of prime factors of n (counted with multiplicity) is 2 times a prime.

4, 8, 9, 21, 25, 30, 32, 33, 36, 49, 57, 69, 70, 84, 85, 93, 100, 102, 120, 121, 128, 129, 133, 135, 144, 145, 162, 169, 174, 177, 182, 190, 205, 213, 217, 228, 237, 238, 246, 249, 253, 260, 265, 286, 289, 308, 309, 310, 312, 318, 340, 351, 361, 372, 393, 406

Offset: 1

Author

Michel Lagneau, Jun 02 2012

Keywords

• nonn

Comments

The numbers A100118(n)^2 are in the sequence.

Examples

			36 is in the sequence because 36 = 2^2 * 3^2 => sum of prime factors = 2*2+3*2 = 10 = 2*5 where 5 is prime.
		

Crossrefs

Cf. A001414, A100118.

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)/2,prime)= true then printf(`%d, `,m):else fi:od:

Mathematica

L = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[PrimeQ[w/2], AppendTo[L, k]], {k, 2, 500}]; L

Formula

sopfr(n) = 2*p, p prime.