A373105 a(n) = sigma_10(n^2)/sigma_5(n^2).

1, 993, 58807, 1016801, 9762501, 58395351, 282458443, 1041204193, 3472494301, 9694163493, 25937263551, 59795016407, 137858120557, 280481233899, 574103396307, 1066193093601, 2015992480593, 3448186840893, 6131063781703, 9926520779301

Offset

1,2

Links

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

Formula

a(n) = Sum_{1 <= x_1, x_2, x_3, x_4, x_5 <= n} ( n/gcd(x_1, x_2, x_3, x_4, x^5, n) )^5.

a(n) = Sum_{d|n} mu(n/d) * (n/d)^5 * sigma_10(d).

From Amiram Eldar, May 25 2024: (Start)

Multiplicative with a(p^e) = (p^(10*e+5) + 1)/(p^5 + 1).

Dirichlet g.f.: zeta(s)*zeta(s-10)/zeta(s-5).

Sum_{k=1..n} a(k) ~ c * n^11 / 11, where c = zeta(11)/zeta(6) = 0.9834383562... . (End)

Mathematica

f[p_, e_] := (p^(10*e+5) + 1)/(p^5 + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, May 25 2024 *)

Prog

(PARI) a(n) = sigma(n^2, 10)/sigma(n^2, 5);
(PARI) a(n) = sumdiv(n, d, moebius(n/d)*(n/d)^5*sigma(d, 10));

Crossrefs

Cf. A057660, A084218, A084220, A372966.

Cf. A371491, A371878, A373007, A373103.

Cf. A013664, A013669.

Sequence in context: A181707 A035857 A028513 * A267119 A210315 A182694

Adjacent sequences: A373102 A373103 A373104 * A373106 A373107 A373108

Keyword

nonn,mult

Author

Seiichi Manyama, May 25 2024

Status

approved