A357689 a(n) = n/A204455(n), where A204455(n) is the product of odd noncomposite divisors of n.

1, 2, 1, 4, 1, 2, 1, 8, 3, 2, 1, 4, 1, 2, 1, 16, 1, 6, 1, 4, 1, 2, 1, 8, 5, 2, 9, 4, 1, 2, 1, 32, 1, 2, 1, 12, 1, 2, 1, 8, 1, 2, 1, 4, 3, 2, 1, 16, 7, 10, 1, 4, 1, 18, 1, 8, 1, 2, 1, 4, 1, 2, 3, 64, 1, 2, 1, 4, 1, 2, 1, 24, 1, 2, 5, 4, 1, 2, 1, 16, 27, 2, 1, 4, 1, 2, 1, 8, 1, 6, 1, 4, 1, 2, 1, 32, 1, 14, 3, 20

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n)*A204455(n) = n.

a(n) = EvenPart(n)*A003557(OddPart(n)). - Peter Munn, Oct 09 2022

Multiplicative with a(p^e) = p^(e-1) if p > 2 and a(2^e) = 2^e. - Amiram Eldar, Oct 10 2022

Example

n = A204455(n)*a(n): 1 = 1*1, 2 = 1*2, 3 = 3*1, 4 = 1*4, 5 = 5*1, 6 = 3*2.

Mathematica

f[p_, e_] := p^(e - If[p == 2, 0, 1]); a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 10 2022 *)

Prog

(Magma) [(2*n)/&*PrimeDivisors(2*n): n in [1..100]];
(Magma) [n/&*[d: d in Divisors(n) | d*#[m: m in [0..n-1] | -m^d mod d eq m] eq
  #[m: m in [0..n-1] | m^d mod d eq m]]: n in [1..100]];

Crossrefs

Cf. A000265, A003557, A006519, A204455.

Equals A324873 up to a(32) = 32.

Sequence in context: A087258 A333763 A076775 * A324873 A325566 A218621

Adjacent sequences: A357686 A357687 A357688 * A357690 A357691 A357692

Keyword

nonn,mult,easy

Author

Juri-Stepan Gerasimov, Oct 09 2022

Status

approved