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Search: id:A119769
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| A119769 |
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a(n) = (n-1)!*sum{1<=k<=n, GCD(k,n)=1} H(k), where H(k) = sum{j=1 to k} 1/j, the k-th harmonic number. |
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+0
1
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| 1, 1, 5, 17, 154, 394, 8028, 38856, 490992, 2995632, 80627040, 355102560, 13575738240, 88085232000, 1686518184960, 26227674547200, 867718162483200, 5518758670387200, 309920046408806400, 2608370444213452800
(list; graph; listen)
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OFFSET
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1,3
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MAPLE
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H := proc(n::integer) RETURN( sum('1/j', j=1..n) ) ; end: A119769 := proc(n::integer) local resul, k ; resul :=0 ; for k from 1 to n do if gcd(k, n) = 1 then resul := resul+H(k) ; fi ; od : RETURN((n-1)!*resul) ; end: for n from 1 to 30 do printf("%d, ", A119769(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2006
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MATHEMATICA
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f[n_] := (n - 1)!Sum[If[GCD[k, n] == 1, HarmonicNumber[k], 0], {k, n}]; Array[f, 21] -Robert G. Wilson v (rgwv(at)rgwv.com), Jun 20 2006
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PROGRAM
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; ; PLT DrScheme - Joshua Zucker (joshua.zucker@stanfordalumni.org), Jun 21 2006
; ; harmonic is the sum of reciprocals, ! has the obvious definition.
(define (A119769 n)
(* (! (sub1 n))
(apply + (map harmonic (filter (lambda (k) (= 1 (gcd n k))) (build-list n (lambda (k) (add1 k))))))))
(build-list 30 (lambda (n) (A119769 (add1 n))))
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CROSSREFS
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Sequence in context: A076448 A096310 A071057 this_sequence A090886 A097490 A053678
Adjacent sequences: A119766 A119767 A119768 this_sequence A119770 A119771 A119772
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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), Jun 19 2006
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jun 20 2006
More terms from Robert G. Wilson v (rgwv(at)rgwv.com), R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 20 2006
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