

A100118


Numbers whose sum of prime factors is prime (counted with multiplicity).


16



2, 3, 5, 6, 7, 10, 11, 12, 13, 17, 19, 22, 23, 28, 29, 31, 34, 37, 40, 41, 43, 45, 47, 48, 52, 53, 54, 56, 58, 59, 61, 63, 67, 71, 73, 75, 76, 79, 80, 82, 83, 88, 89, 90, 96, 97, 99, 101, 103, 104, 107, 108, 109, 113, 117, 118, 127, 131, 136, 137, 139, 142, 147, 148, 149
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OFFSET

1,1


COMMENTS

Numbers n such that integer log of n is a prime number.
As in A001414, denote sopfr(n) the integer log of n. Since sopfr(p)=p, the sequence includes all prime numbers.
See A046363 for the analogue excluding prime numbers.  Hieronymus Fischer, Oct 20 2007


LINKS

Jayanta Basu, Table of n, a(n) for n = 1..10000


EXAMPLE

e.g. 40 = 2^3*5 and 2*3+5=11 is a prime number.


MATHEMATICA

L = {}; Do[ww = Transpose[FactorInteger[k]]; w = ww[[1]].ww[[2]]; If[PrimeQ[w], AppendTo[L, k]], {k, 2, 500}]; L
Select[Range[150], PrimeQ[Total[Times @@@ FactorInteger[#]]] &] (* Jayanta Basu, Aug 11 2013 *)


PROG

(PARI) is(n)=my(f=factor(n)); isprime(sum(i=1, #f~, f[i, 1]*f[i, 2])) \\ Charles R Greathouse IV, Sep 21 2013


CROSSREFS

Cf. A001414, A046363.
Sequence in context: A024899 A114518 A066940 * A028781 A136149 A101882
Adjacent sequences: A100115 A100116 A100117 * A100119 A100120 A100121


KEYWORD

easy,nonn


AUTHOR

Carlos Alves, Dec 26 2004


STATUS

approved



