A139556 a(n) = sum of the prime-powers (including 1) that each are <= n and are coprime to n.

1, 1, 3, 4, 10, 6, 15, 16, 27, 20, 39, 24, 50, 42, 46, 49, 79, 54, 96, 80, 96, 74, 115, 96, 133, 120, 151, 153, 190, 120, 219, 220, 232, 203, 245, 181, 282, 238, 267, 227, 319, 252, 360, 330, 334, 318, 403, 349, 443, 407, 443, 424, 499, 451, 511, 434, 494, 461

Offset: 1

Author

Leroy Quet, Apr 27 2008

Keywords

• nonn

Examples

			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.
		

Links

• Robert Price, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000961, A139555.

Programs

Maple

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

Mathematica

f[n_] := Plus @@ Select[Range@ n, Length@ FactorInteger@ # == 1 == GCD[n, # ] &]; Array[f, 58] (* Robert G. Wilson v *)

Extensions

More terms from R. J. Mathar, May 12 2008