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 A139556 a(n) = sum of the prime-powers (including 1) that each are <= n and are coprime to n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS 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

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)