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%I #9 Oct 03 2015 23:20:12
%S 1,1,3,4,10,6,15,16,27,20,39,24,50,42,46,49,79,54,96,80,96,74,115,96,
%T 133,120,151,153,190,120,219,220,232,203,245,181,282,238,267,227,319,
%U 252,360,330,334,318,403,349,443,407,443,424,499,451,511,434,494,461
%N a(n) = sum of the prime-powers (including 1) that each are <= n and are coprime to n.
%e All the positive integers <= 21 that are coprime to 21 are 1,2,4,5,8,10,11,13,16,17,19,20. Of these integers, only 1,2,4,5,8,11,13,16,17,19 are prime-powers. The sum of these prime-powers is 1+2+4+5+8+11+13+16+17+19 = 96; so a(21) = 96.
%p isA000961 := proc(n) if n = 1 or isprime(n) then true; else RETURN(nops(ifactors(n)[2]) =1) ; fi ; end: A139556 := proc(n) local a,i; a := 0 ; for i from 1 to n do if isA000961(i) and gcd(i,n) = 1 then a := a+i ; fi ; od: a ; end: seq(A139556(n),n=1..100) ; # _R. J. Mathar_, May 12 2008
%t f[n_] := Plus @@ Select[Range@ n, Length@ FactorInteger@ # == 1 == GCD[n, # ] &]; Array[f, 58] (* _Robert G. Wilson v_ *)
%Y Cf. A139555.
%K nonn
%O 1,3
%A _Leroy Quet_, Apr 27 2008
%E More terms from _R. J. Mathar_, May 12 2008
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