cp's OEIS Frontend

A163517 If m-th composite is the product of k1-th prime, k2-th prime,..,kr-th prime and prime=k1+k2+..+kr then set a(n)=m.

%I A163517 #9 Apr 06 2014 08:35:31
%S A163517 1,2,3,7,8,10,11,14,16,20,21,23,28,29,30,34,37,39,41,42,49,51,52,57,
%T A163517 67,68,70,71,78,83,88,91,93,96,106,108,110,115,116,120,123,130,133,
%U A163517 136,139,145,150,157,160,162,166,167,171,173,177,179,180,181,182,184,188,191
%N A163517 If m-th composite is the product of k1-th prime, k2-th prime,..,kr-th prime and prime=k1+k2+..+kr then set a(n)=m.
%e A163517 1st composite=4=2*2=prime(1)*prime(1) and 1+1=2 prime, so a(1)=1.
%e A163517 2nd composite=6=2*3=prime(1)*prime(2) and 1+2=3 prime, so a(2)=2.
%e A163517 3rd composite=8=2*2*2=prime(1)*prime(1)*prime(1) and 1+1+1=3 prime, so a(3)=3.
%e A163517 7th composite=14=2*7=prime(1)*prime(4) and 1+4=5 prime, so a(4)=7.
%p A163517 A056239 := proc(n) pfs := ifactors(n)[2] ; add ( op(2,d)*numtheory[pi](op(1,d)), d=pfs) ; end: A002808 := proc(n) option remember ; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a) ; fi; od: fi; end: for n from 1 to 300 do if isprime(A056239( A002808(n))) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Aug 01 2009
%Y A163517 Cf. A000040, A002808, A061395.
%K A163517 nonn
%O A163517 1,2
%A A163517 _Juri-Stepan Gerasimov_, Jul 30 2009
%E A163517 Values from a(16) on corrected by _R. J. Mathar_, Aug 01 2009