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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20736

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

Formula

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

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

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 *)

Prog

(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]))); };

Crossrefs

Cf. A000265, A331737, A331739.

Sequence in context: A076933 A071974 A056622 * A306333 A237983 A335977

Adjacent sequences: A331735 A331736 A331737 * A331739 A331740 A331741

Keyword

nonn,mult

Author

Antti Karttunen, Feb 02 2020

Status

approved