%I #11 Feb 24 2024 16:16:24

%S 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,

%T 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,

%U 4,8,2,9,2,4,6,6,4,8,2,8,4,4,2,12,4,4,4

%N The number of exponentially odious divisors of n.

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

%C 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.

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

%H Amiram Eldar, <a href="/A366901/b366901.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t 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]

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

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

%Y Cf. A000005, A000069, A004709, A115384, A270428, A366903, A366905.

%Y Cf. A049599, A282446, A365551, A353898.

%Y Similar sequences: A325837, A353898, A365680, A366902.

%K nonn,easy,mult

%O 1,2

%A _Amiram Eldar_, Oct 27 2023