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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 16:10 EST 2014. Contains 250079 sequences.