A331738 Multiplicative with a(p^e) = p^(e-A000265(e)), where A000265(x) gives the odd part of x.

1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 8, 1, 3, 1, 2, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 8, 7, 5, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 8, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 5, 2, 1, 1, 1, 8, 27, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 7, 3, 10, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Feb 02 2020

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20736
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A000265, A331737, A331739.

Programs

Mathematica

f[p_, e_] := p^(e - e/2^IntegerExponent[e, 2]); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 24 2022 *)

PARI

A000265(n) = (n>>valuation(n,2));
A331738(n) = { my(f = factor(n)); prod(k=1, #f~, f[k, 1]^(f[k, 2]-A000265(f[k, 2]))); };

Formula

Multiplicative with a(p^e) = p^A331739(e).

a(n) = n / A331737(n).