A336651 Odd part of n divided by its largest squarefree divisor.

1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 5, 1, 1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 5, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 7, 3, 5, 1, 1, 1, 1, 1

Offset

1,9

Comments

The name can be parsed either as "Odd part of {n divided by its largest squarefree divisor}" or "Odd part of n, divided by its largest squarefree divisor". Because A000265 and A003557 commute, both interpretations yield equal results.

Links

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

Formula

Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = p^(e-1).

a(n) = A003557(A000265(n)) = A000265(A003557(n)).

a(n) = A000265(n) / A204455(n).

A000203(a(n)) = A336649(n).

Dirichlet g.f.: (1 - 1/(2^s-1)^2) * zeta(s-1) * Product_{p prime} (1 - 1/p^(s-1) + 1/p^s). - Amiram Eldar, Sep 14 2023

Mathematica

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

Prog

(PARI) A336651(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i, 1], 1, f[i, 1]^(f[i, 2]-1))); };

Crossrefs

Cf. A000203, A000265, A003557, A007947, A336649, A336652.

Sequence in context: A030576 A101874 A318449 * A066715 A082457 A356307

Adjacent sequences: A336648 A336649 A336650 * A336652 A336653 A336654

Keyword

nonn,easy,mult

Author

Antti Karttunen, Jul 30 2020

Status

approved