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
KEYWORD
nonn
AUTHOR
Carlos Alves, Dec 26 2004
STATUS
approved