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 A100118 Numbers whose sum of prime factors is prime (counted with multiplicity). 21
 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 analog excluding prime numbers. - Hieronymus Fischer, Oct 20 2007 These numbers may be arranged in a family of posets of triangles of multiarrows (see link and example). - Gus Wiseman, Sep 14 2016 LINKS Jayanta Basu, Table of n, a(n) for n = 1..10000 Gus Wiseman, lattice form posets indexed by A100118 EXAMPLE 40 = 2^3*5 and 2*3 + 5 = 11 is a prime number. These numbers correspond to multiarrows in the multiorder of partitions of prime numbers into prime parts. For example: 2:2<=(2), 3:3<=(3), 6:5<=(2,3), 5:5<=(5), 12:7<=(2,2,3), 10:7<=(2,5), 7:7<=(7), 48:11<=(2,2,2,2,3), 52:11<=(2,3,3,3), 40:11<=(2,2,2,5), 45:11<=(3,3,5), 28:11<=(2,2,7), 11:11<=(11). - Gus Wiseman, Sep 14 2016. MAPLE for n from 1 to 200 do     if isprime(A001414(n)) then         printf("%d, ", n);     end if; end do: # R. J. Mathar, Sep 09 2015 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, A056768, A276687. Sequence in context: A024899 A114518 A066940 * A028781 A136149 A101882 Adjacent sequences:  A100115 A100116 A100117 * A100119 A100120 A100121 KEYWORD nonn AUTHOR Carlos Alves, Dec 26 2004 STATUS approved

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