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A077457 a(n) = sigma_4(n^4)/sigma_2(n^4). 1
1, 205, 5905, 52429, 375601, 1210525, 5649505, 13421773, 38742049, 76998205, 212601841, 309593245, 810932305, 1158148525, 2217923905, 3435973837, 6951703105, 7942120045, 16936647121, 19692384829, 33360327025, 43583377405, 78163228705, 79255569565, 146719125601 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
sigma_y(n^x) divides sigma_x(n^x) for all n if y divides x.
LINKS
FORMULA
a(n) = A001159(n^4)/A001157(n^4).
Multiplicative with a(p^e) = (p^(8*e+2) + 1)/(p^2 + 1). - Amiram Eldar, Sep 09 2020
Sum_{k=1..n} a(k) ~ c * n^9, where c = (zeta(9)/9) * Product_{p prime} (1 - 1/p^3 + 1/p^5 - 1/p^7) = 0.09549806119... . - Amiram Eldar, Oct 28 2022
MATHEMATICA
f[p_, e_] := (p^(8*e+2) + 1)/(p^2 + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 25] (* Amiram Eldar, Sep 09 2020 *)
PROG
(PARI) a(n)=sumdiv(n^4, d, d^4)/sumdiv(n^4, d, d^2)
(PARI) a(n) = my(f=factor(n^4)); sigma(f, 4)/sigma(f, 2); \\ Michel Marcus, Sep 09 2020
CROSSREFS
Sequence in context: A203896 A203889 A226564 * A060892 A359498 A203862
KEYWORD
nonn,easy,mult
AUTHOR
Benoit Cloitre, Nov 30 2002
STATUS
approved

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Last modified April 13 05:19 EDT 2024. Contains 371639 sequences. (Running on oeis4.)