A378930 a(n) = n * d(n) / gcd(n, d(n))^2, where d = A000005.

1, 1, 6, 12, 10, 6, 14, 2, 3, 10, 22, 2, 26, 14, 60, 80, 34, 3, 38, 30, 84, 22, 46, 3, 75, 26, 108, 42, 58, 60, 62, 48, 132, 34, 140, 4, 74, 38, 156, 5, 82, 84, 86, 66, 30, 46, 94, 120, 147, 75, 204, 78, 106, 108, 220, 7, 228, 58, 118, 5, 122, 62, 42, 448, 260

Offset: 1

Author

Viliam Furík, Dec 11 2024

Keywords

• nonn

Links

• Viliam Furík, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A009191, A009230, A038040.

Programs

Maple

a:= n-> (d-> n*d/igcd(n,d)^2)(numtheory[tau](n)):
seq(a(n), n=1..65);  # Alois P. Heinz, Dec 11 2024

Mathematica

a[n_]:= n * DivisorSigma[0,n]/GCD[n, DivisorSigma[0,n]]^2; Array[a,65] (* Stefano Spezia, Dec 11 2024 *)

PARI

a(n) = my(d = numdiv(n)); n * d / gcd(n, d)^2; \\ Amiram Eldar, Dec 11 2024

Formula

a(n) = A038040(n)/A009191(n)^2.

a(n) = A009230(n)/A009191(n).