A367515 The number of unitary divisors of n that are exponentially odious numbers (A270428).

1, 2, 2, 2, 2, 4, 2, 1, 2, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 4, 4, 4, 2, 2, 2, 4, 1, 4, 2, 8, 2, 1, 4, 4, 4, 4, 2, 4, 4, 2, 2, 8, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 2, 4, 2, 4, 4, 2, 8, 2, 4, 4, 1, 4, 8, 2, 4, 4, 8, 2, 2, 2, 4, 4, 4, 4, 8, 2, 4, 2, 4, 2, 8, 4, 4, 4

Offset: 1

Author

Amiram Eldar, Nov 21 2023

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A001285, A262675, A270428, A293439.

Similar sequences: A034444, A055076, A056624, A366901, A366902, A367516.

Programs

Mathematica

f[p_, e_] := If[OddQ[DigitCount[e, 2, 1]], 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PARI

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

Python

from sympy import factorint
def A367515(n): return 1<Chai Wah Wu, Nov 23 2023

Formula

Multiplicative with a(p^e) = A001285(e).

a(n) = A034444(n)/A367516(n).

a(n) = 2^A293439(n).

a(n) >= 1, with equality if and only if n is an exponentially evil number (A262675).

a(n) <= A034444(n), with equality if and only if n is an exponentially odious number (A270428).