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

1,2

Links

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

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).

Mathematica

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

Prog

(PARI) a(n) = vecprod(apply(x -> hammingweight(x)%2+1, factor(n)[, 2]));
(Python)
from sympy import factorint
def A367515(n): return 1<<sum(1 for e in factorint(n).values() if e.bit_count()&1) # Chai Wah Wu, Nov 23 2023

Crossrefs

Cf. A001285, A262675, A270428, A293439.

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

Sequence in context: A122857 A109810 A365498 * A122066 A053238 A227783

Adjacent sequences: A367512 A367513 A367514 * A367516 A367517 A367518

Keyword

nonn,easy,mult

Author

Amiram Eldar, Nov 21 2023

Status

approved