A193348 Number of odd divisors of tau(n).

1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 3

Offset: 1

Author

Michel Lagneau, Jul 23 2011

Keywords

• nonn
• easy

Examples

			a(36) = 3 because tau(36) = 9 and the 3 odd divisors are {1, 3, 9}.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A001227, A010553, A036537, A193349.

Programs

Mathematica

a[n_] := Block[{d = Divisors[DivisorSigma[0,n]]}, Count[OddQ[d], True]]; Table[a[n], {n, 80}]

PARI

a(n)=sumdiv(sigma(n,0),d,d%2);

PARI

a(n)=n=numdiv(n);numdiv(n>>valuation(n,2)) \\ Charles R Greathouse IV, Jul 30 2011

Formula

a(n) = A001227(A000005(n)). - Reinhard Zumkeller, Jul 25 2011

From Amiram Eldar, Aug 12 2024: (Start)

a(n) = 1 if and only if n is in A036537.

a(n) = A010553(n) if and only if n is a square. (End)