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A193335
Number of odd divisors of sigma(n).
2
1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 2, 2, 2, 2, 2, 3, 4, 2, 4, 1, 3, 2, 4, 2, 4, 2, 2, 4, 3, 1, 6, 2, 4, 2, 4, 2, 4, 2, 6, 4, 2, 2, 4, 4, 3, 2, 2, 4, 4, 3, 3, 4, 4, 3, 4, 2, 6, 4, 4, 2, 2, 2, 2, 4, 3, 2, 6, 2, 3, 3, 8, 2, 4, 2, 4, 2, 4, 2, 4
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A001227(A000203(n)). - Michel Marcus, Jan 14 2014
EXAMPLE
a(8) = 4 because sigma(8) = 15 and the 4 odd divisors are { 1, 3, 5, 15}.
MATHEMATICA
f[n_] := Block[{d = Divisors[DivisorSigma[1, n]]}, Count[OddQ[d], True]]; Table[f[n], {n, 80}]
Table[Count[Divisors[DivisorSigma[1, n]], _?OddQ], {n, 80}] (* Harvey P. Dale, Jul 06 2019 *)
odd[n_] := DivisorSigma[0, n / 2^IntegerExponent[n, 2]]; a[n_] := odd[DivisorSigma[1, n]]; Array[a, 100] (* Amiram Eldar, Jul 06 2022 *)
PROG
(PARI) a(n)=sumdiv(sigma(n, 1), d, d%2);
(PARI) a(n)=n=sigma(n); numdiv(n>>valuation(n, 2)) \\ Charles R Greathouse IV, Jul 30 2011
CROSSREFS
Cf. A000203 (sigma), A001227.
Sequence in context: A335283 A126865 A104640 * A016727 A335420 A241318
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 23 2011
STATUS
approved