The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A373129 a(n) = Sum_{1 <= x_1, x_2 <= n} sigma( n/gcd(x_1, x_2, n) ). 1
 1, 10, 33, 94, 145, 330, 385, 814, 969, 1450, 1441, 3102, 2353, 3850, 4785, 6766, 5185, 9690, 7201, 13630, 12705, 14410, 12673, 26862, 18745, 23530, 26889, 36190, 25201, 47850, 30721, 55150, 47553, 51850, 55825, 91086, 51985, 72010, 77649, 118030, 70561, 127050 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{1 <= x_1, x_2 <= n} sigma( ( gcd(x_1, n)/gcd(x_1, x_2, n) )^2 ). a(n) = Sum_{d|n} J_2(d) * sigma(d), where the Jordan totient function J_2(n) = A007434(n). From Amiram Eldar, May 26 2024: (Start) Multiplicative with a(p^e) = (p^(3*e+2)*(p+1) - p^(2*e)*(p^2+p+1) + p)/(p^3-1). Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = zeta(4) * Product_{p prime} (1 + 1/p^2 - 1/p^3) = 1.41347980562116709395... . (End) MATHEMATICA f[p_, e_] := (p^(3*e + 2)*(p+1) - p^(2*e)*(p^2+p+1) + p)/(p^3-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 26 2024 *) PROG (PARI) J(n, k) = sumdiv(n, d, d^k*moebius(n/d)); a(n, k=2, m=1) = sumdiv(n, d, J(d, k)*sigma(d^m)); CROSSREFS Cf. A007434, A013662, A064987, A350156. Sequence in context: A003012 A020478 A094170 * A004638 A211033 A020479 Adjacent sequences: A373126 A373127 A373128 * A373130 A373131 A373132 KEYWORD nonn,mult AUTHOR Seiichi Manyama, May 26 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 4 22:06 EDT 2024. Contains 374934 sequences. (Running on oeis4.)