A382291 a(n) = A037445(n)/A034444(n).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset: 1

Author

Amiram Eldar, Mar 21 2025

Keywords

• nonn
• easy
• mult

Comments

First differs from A368168 at n = 64, and from A359411, A367516 and A368979 at n = 128.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A034444, A037445, A138302, A243036, A382290, A382292.

Cf. A359411, A367516, A368168, A368979.

Programs

Mathematica

f[p_, e_] := 2^(DigitCount[e, 2, 1] - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 105]

PARI

a(n) = vecprod(apply(x -> 1 << (hammingweight(x)-1), factor(n)[, 2]));

Formula

a(n) = 2^A382290(n).

Multiplicative with a(p^e) = 2^(A000120(e)-1) = A048896(e-1) (= A243036(e) for e >= 2).

a(n) >= 1, with equality if and only if n is in A138302.

a(n) = 2 if and only if n is in A382292.