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

1,3

Links

Table of n, a(n) for n=1..58.

Example

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.

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 *)

Crossrefs

Cf. A139555.

Sequence in context: A014411 A247372 A143443 * A191150 A023896 A328711

Adjacent sequences: A139553 A139554 A139555 * A139557 A139558 A139559

Keyword

nonn

Author

Leroy Quet, Apr 27 2008

Extensions

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

Status

approved