A349273 Number of odd divisors of prime(n) - 1.

1, 1, 1, 2, 2, 2, 1, 3, 2, 2, 4, 3, 2, 4, 2, 2, 2, 4, 4, 4, 3, 4, 2, 2, 2, 3, 4, 2, 4, 2, 6, 4, 2, 4, 2, 6, 4, 5, 2, 2, 2, 6, 4, 2, 3, 6, 8, 4, 2, 4, 2, 4, 4, 4, 1, 2, 2, 8, 4, 4, 4, 2, 6, 4, 4, 2, 8, 4, 2, 4, 2, 2, 4, 4, 8, 2, 2, 6, 3, 4, 4, 8, 4, 4, 4, 4, 2, 4, 4, 8, 2, 2, 6, 6, 4

Offset

1,4

Comments

a(n) is odd if and only if prime(n) is in A249410. - Jianing Song, Nov 14 2021

Links

Table of n, a(n) for n=1..95.

Formula

a(n) = A001227(A006093(n)).

Mathematica

a[n_] := DivisorSigma[0, (k = Prime[n] - 1)/2^IntegerExponent[k, 2]]; Array[a, 100] (* Amiram Eldar, Jun 03 2021 *)

Prog

(Magma) [NumberOfDivisors(p-1)/Valuation(2*p-2, 2): p in PrimesUpTo(500)];
(Python)
from sympy import divisors, prime
def a(n): return sum(d%2 for d in divisors(prime(n)-1))
print([a(n) for n in range(1, 96)]) # Michael S. Branicky, Jul 04 2021
(PARI) a(n) = sumdiv(prime(n)-1, d, d%2); \\ Michel Marcus, Dec 18 2021

Crossrefs

Cf. A000040, A001227, A006093, A249410.

Sequence in context: A260372 A037180 A241675 * A091222 A316506 A294884

Adjacent sequences: A349270 A349271 A349272 * A349274 A349275 A349276

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Nov 12 2021

Status

approved