

A107737


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


3



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
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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



