A372997 a(n) = Sum_{k=1..n} tau( (n/gcd(k,n))^3 ).

1, 5, 9, 19, 17, 45, 25, 59, 51, 85, 41, 171, 49, 125, 153, 163, 65, 255, 73, 323, 225, 205, 89, 531, 157, 245, 231, 475, 113, 765, 121, 419, 369, 325, 425, 969, 145, 365, 441, 1003, 161, 1125, 169, 779, 867, 445, 185, 1467, 319, 785, 585, 931, 209, 1155, 697, 1475

Offset

1,2

Links

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

Formula

If p is prime, a(p) = 4*p - 3.

a(n) = Sum_{d|n} phi(d) * tau(d^3).

Multiplicative with a(p^e) = (3 - (3*e+4)*p^e + (3*e+1)*p^(e+1))/(p-1). - Amiram Eldar, May 21 2024

Mathematica

f[p_, e_] := (3 - (3*e+4)*p^e + (3*e+1)*p^(e+1))/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 21 2024 *)

Prog

(PARI) a(n) = sumdiv(n, d, eulerphi(d)*numdiv(d^3));

Crossrefs

Cf. A062380, A062949, A372999.

Cf. A000005, A000010, A344221.

Sequence in context: A116453 A046578 A046590 * A344746 A226663 A023521

Adjacent sequences: A372994 A372995 A372996 * A372998 A372999 A373000

Keyword

nonn,mult

Author

Seiichi Manyama, May 19 2024

Status

approved