A366901 - OEIS

A366901

The number of exponentially odious divisors of n.

1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 4, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 8, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 4, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 8, 4, 4, 2, 12, 4, 4, 4

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OFFSET

1,2

COMMENTS

First differs from A049599 and A282446 at n = 32, from A365551 at n = 64, and from A353898 at n = 128.

The number of divisors of n that are exponentially odious numbers (A270428), i.e., numbers having only odious (A000069) exponents in their canonical prime factorization.

The sum of these divisors is A366903(n) and the largest of them is A366905(n).

LINKS

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

FORMULA

Multiplicative with a(p^e) = A115384(e) + 1.

a(n) <= A000005(n), with equality if and only if n is a cubefree number (A004709).

MATHEMATICA

f[p_, e_] := Floor[e/2] + If[OddQ[e] || EvenQ[DigitCount[e + 1, 2, 1]], 1, 0] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PROG

(PARI) s(n) = 1 + n\2 + (n%2 || hammingweight(n+1)%2==0); \\ after Charles R Greathouse IV at A115384

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

CROSSREFS