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
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20736
- Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Programs
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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]))); };