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Search: id:A139556
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| A139556 |
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a(n) = sum of the prime-powers (including 1) that each are <= n and are coprime to n. |
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+0
2
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| 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; listen)
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OFFSET
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1,3
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EXAMPLE
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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.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), May 12 2008
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MATHEMATICA
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f[n_] := Plus @@ Select[Range@ n, Length@ FactorInteger@ # == 1 == GCD[n, # ] &]; Array[f, 58] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A139555.
Adjacent sequences: A139553 A139554 A139555 this_sequence A139557 A139558 A139559
Sequence in context: A063930 A014411 A143443 this_sequence A023896 A128488 A117781
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Apr 27 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
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