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A357689
a(n) = n/A204455(n), where A204455(n) is the product of odd noncomposite divisors of n.
1
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
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
Equals A324873 up to a(32) = 32.
Sequence in context: A087258 A333763 A076775 * A324873 A325566 A218621
KEYWORD
nonn,mult,easy
AUTHOR
STATUS
approved