A349273 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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 *)

Count[Divisors[#-1], _?OddQ]&/@Prime[Range[100]] (* Harvey P. Dale, Jan 22 2024 *)