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

1,1

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Prime Factorization

Example

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

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 *)

Crossrefs

Cf. A008474, A107738.

Sequence in context: A047278 A242204 A172209 * A045138 A067704 A284889

Adjacent sequences: A107734 A107735 A107736 * A107738 A107739 A107740

Keyword

nonn

Author

Zak Seidov, May 23 2005

Status

approved