A077456 a(n) = sigma_5(n^5)/sigma(n^5).

1, 549791, 2337334621, 567767102431, 76323251878121, 1285045538614211, 68398022066406901, 595065340418751455, 8138648440293876241, 41961836973324022711, 611595047235520833101, 1327061705176829563651, 17543094367661056941241, 37604616949911916507691

Offset: 1

Author

Benoit Cloitre, Nov 30 2002

Keywords

• nonn
• easy
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A000584, A001160, A057660, A077454, A077455.

Programs

Mathematica

f[p_, e_] := (p^(20*e+4) + p^(15*e+3) + p^(10*e+2) + p^(5*e+1) + 1)/(p^4 + p^3 + p^2 + p + 1); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 20] (* Amiram Eldar, Sep 09 2020 *)
Table[DivisorSigma[5,n^5]/DivisorSigma[1,n^5],{n,20}] (* Harvey P. Dale, Mar 05 2022 *)

PARI

a(n)=sumdiv(n^5,d,d^5)/sigma(n^5)

PARI

a(n) = my(f=factor(n^5)); sigma(f, 5)/sigma(f); \\ Michel Marcus, Sep 09 2020

Formula

a(n) = A001160(n^5)/A000203(n^5).

Multiplicative with a(p^e) = (p^(20*e+4) + p^(15*e+3) + p^(10*e+2) + p^(5*e+1) + 1)/(p^4 + p^3 + p^2 + p + 1). - Amiram Eldar, Sep 09 2020