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A077455
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a(n) = sigma_4(n^4)/sigma(n^4).
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4
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1, 2255, 360205, 8965359, 195688121, 812262275, 11869610005, 36654862063, 190649623129, 441276712855, 2853329308061, 3229367138595, 21506735660905, 26765970561275, 70487839624805, 150121132912367, 548357292625505, 429914900155895, 2096841596815405, 1754414256800439
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OFFSET
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1,2
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A001158(n^4)/A000203(n^4).
Multiplicative with a(p^e) = (p^(12*e+3) + p^(8*e+2) + p^(4*e+1) + 1)/(p^3 + p^2 + p + 1). - Amiram Eldar, Sep 09 2020
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EXAMPLE
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a(2) = sigma_4(2^4)/sigma(2^4) = 69905/31 = 2255.
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MATHEMATICA
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f[p_, e_] := (p^(12*e+3) + p^(8*e+2) + p^(4*e+1) + 1)/(p^3 + p^2 + p + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 20] (* Amiram Eldar, Sep 09 2020 *)
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PROG
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(PARI) a(n)=sumdiv(n^4, d, d^4)/sigma(n^4)
(PARI) a(n) = my(f=factor(n^4)); sigma(f, 4)/sigma(f); \\ Michel Marcus, Sep 09 2020
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CROSSREFS
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Cf. A000203, A000583, A001158, A057660, A077454, A077456.
Sequence in context: A287701 A123297 A251944 * A068754 A222951 A035873
Adjacent sequences: A077452 A077453 A077454 * A077456 A077457 A077458
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KEYWORD
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nonn,easy,mult
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AUTHOR
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Benoit Cloitre, Nov 30 2002
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STATUS
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approved
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