%I #8 Feb 10 2019 23:02:53
%S 1,4,8,9,10,12,15,20,21,24,26,28,33,34,35,38,40,42,45,46,49,50,51,55,
%T 56,58,60,63,66,68,70,72,74,75,80,81,84,88,90,92,96,98,99,100,102,104,
%U 105,106,108,110,117,118,119,121,123,124,128,129,130,133,136,140,142,143
%N Nonprimes k such that the sum of prime factors of composite(k) is an even composite.
%e 1 (nonprime) is a term because composite(1) = 4 = 2*2 and 2 + 2 = 4 is an even composite;
%e 4 (nonprime) is a term because composite(4) = 9 = 3*3 and 3 + 3 = 6 is an even composite;
%e 8 (nonprime) is a term because composite(8) = 15 = 3*5 and 3 + 5 = 8 is an even composite.
%p pss := proc(n) local a,d ; a := 0 ; for d in ifactors(n)[2] do a := a+ op(2,d)*op(1,d) ; end do: a ; end proc:
%p isA002808 := proc(n) n >= 4 and not isprime(n) ; end proc:
%p A002808 := proc(n) option remember ; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do; end if; end proc:
%p for n from 1 to 400 do if not isprime(n) then c := pss(A002808(n)) ; if type(c,'even') and isA002808(c) then printf("%d,",n) ; end if; end if; end do: # _R. J. Mathar_, May 10 2010
%Y Cf. A000027, A002808, A141468.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Jan 20 2009
%E Corrected (44 removed, 80 inserted) by _R. J. Mathar_, May 10 2010