A107737 Numbers n such that, in prime decomposition of n, sum of all prime factors and their orders is prime.

2, 6, 8, 9, 14, 25, 26, 30, 32, 38, 40, 45, 56, 63, 66, 70, 74, 75, 81, 86, 88, 96, 99, 100, 104, 117, 121, 130, 134, 136, 138, 144, 147, 153, 154, 158, 160, 168, 174, 184, 190, 194, 196, 206, 207, 216, 218, 238, 248, 250, 252, 254, 266, 275, 279, 280, 286, 289

Offset: 1

Author

Zak Seidov, May 23 2005

Keywords

• nonn

Comments

Corresponding primes in A107738. Cf. A008474 If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j).

Examples

			n = 104 OK because 104 = 2^3 * 13^1 => (2+3)+(13+1) = 19 is prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime Factorization

Crossrefs

Cf. A008474, A107738.

Programs

Mathematica

ta=Table[Plus @@ Flatten[FactorInteger[n]], {n, 300}];bb={};Do[If[PrimeQ[t=ta[[i]]], bb=Append[bb, {i, t}]], {i, 300}];tr=Transpose[bb];A107738=tr[[2]];A107737=tr[[1]]
Select[Range[2,300],PrimeQ[Total[Flatten[FactorInteger[#]]]]&] (* Harvey P. Dale, Feb 05 2017 *)