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