%I #19 Aug 22 2024 04:47:42

%S 1,549791,2337334621,567767102431,76323251878121,1285045538614211,

%T 68398022066406901,595065340418751455,8138648440293876241,

%U 41961836973324022711,611595047235520833101,1327061705176829563651,17543094367661056941241,37604616949911916507691

%N a(n) = sigma_5(n^5)/sigma(n^5).

%H Amiram Eldar, <a href="/A077456/b077456.txt">Table of n, a(n) for n = 1..10000</a>

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

%F 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

%t 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 *)

%t Table[DivisorSigma[5,n^5]/DivisorSigma[1,n^5],{n,20}] (* _Harvey P. Dale_, Mar 05 2022 *)

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

%o (PARI) a(n) = my(f=factor(n^5)); sigma(f, 5)/sigma(f); \\ _Michel Marcus_, Sep 09 2020

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

%K nonn,easy,mult

%O 1,2

%A _Benoit Cloitre_, Nov 30 2002