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A091954 Number of odd proper divisors of n. That is, the number of odd divisors of n that are less than n. 9
0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 3, 1, 1, 3, 1, 2, 3, 2, 1, 2, 2, 2, 3, 2, 1, 4, 1, 1, 3, 2, 3, 3, 1, 2, 3, 2, 1, 4, 1, 2, 5, 2, 1, 2, 2, 3, 3, 2, 1, 4, 3, 2, 3, 2, 1, 4, 1, 2, 5, 1, 3, 4, 1, 2, 3, 4, 1, 3, 1, 2, 5, 2, 3, 4, 1, 2, 4, 2, 1, 4, 3, 2, 3, 2, 1, 6, 3, 2, 3, 2, 3, 2, 1, 3, 5, 3, 1, 4, 1, 2, 7, 2, 1, 4, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

From Antti Karttunen, Oct 04 2017: (Start)

a(n) = Sum_{d|n, d<n} A000035(n).

a(n) = A001227(n) - A000035(n).

a(n) = A007814(A293214(n)) = A007814(A293216(n)).

(End)

EXAMPLE

The odd divisors of 15 that are less than 15 are 1, 3 and 5. Therefore there are three odd divisors of 15 that are less than 15.

MATHEMATICA

Count[Most[Divisors[#]], _?OddQ]&/@Range[100] (* Harvey P. Dale, Sep 28 2012 *)

PROG

(PARI) A091954(n) = sumdiv(n, d, (d<n)*(d%2)); \\ Antti Karttunen, Oct 04 2017

CROSSREFS

Cf. A000005, A000035, A032741, A001227, A293214, A293216.

Sequence in context: A007061 A001817 A214973 * A325167 A213408 A183953

Adjacent sequences:  A091951 A091952 A091953 * A091955 A091956 A091957

KEYWORD

easy,nonn

AUTHOR

Mohammad K. Azarian, Mar 12 2004

EXTENSIONS

Corrected and extended by Harvey P. Dale, Sep 28 2012

STATUS

approved

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Last modified April 9 10:52 EDT 2020. Contains 333348 sequences. (Running on oeis4.)