A336649 Sum of divisors of A336651(n) (odd part of n divided by its largest squarefree divisor).

1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 6, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 8, 6, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 6, 1, 1, 1, 1, 1, 40, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 8, 4, 6, 1, 1, 1, 1, 1

Offset

1,9

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

Multiplicative with a(2^e) = 1, a(p^1) = 1 and a(p^e) = (p^e - 1)/(p-1) if e > 1.

a(n) = A000203(A336651(n)) = A335341(A000265(n)).

a(n) = A336652(n) / A204455(n).

Dirichlet g.f.: zeta(s-1) * zeta(s) * (1 - 1/(1-2^s+2^(2*s-1))) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^(2*s-1)). - Amiram Eldar, Dec 18 2023

Mathematica

f[2, e_] := 1; f[p_, e_] := (p^e - 1)/(p-1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Dec 07 2020 *)

Prog

(PARI) A336649(n) = { my(f=factor(n)); prod(i=1, #f~, if((2==f[i, 1])||(1==f[i, 2]), 1, (((f[i, 1]^(f[i, 2]))-1) / (f[i, 1]-1)))); };
(PARI)
A000265(n) = (n>>valuation(n, 2));
A335341(n) = if(1==n, n, sigma(n/factorback(factorint(n)[, 1])));
A336649(n) = A335341(A000265(n));

Crossrefs

Cf. A000203, A000265, A204455, A335341, A336651, A336652.

Sequence in context: A367418 A360164 A360163 * A370703 A365487 A368172

Adjacent sequences: A336646 A336647 A336648 * A336650 A336651 A336652

Keyword

nonn,mult

Author

Antti Karttunen, Jul 30 2020

Status

approved