A193509 Number of odd divisors of Omega(n).

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2

Offset: 1

Author

Michel Lagneau, Jul 29 2011

Keywords

• nonn

Comments

Omega(n) is the number of prime divisors of n counted with multiplicity, A001222 (also called bigomega(n)).

Records are at 2^A053624(n). [Charles R Greathouse IV, Jul 29 2011]

Examples

			a(8) = 2 because Omega(8) = 3 and the 2 odd divisors are {1, 3}.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222.

Programs

Mathematica

f[n_] := Block[{d = Divisors[PrimeOmega[n]]}, Count[OddQ[d], True]]; Table[f[n], {n,80}]

PARI

a(n)=if(n==1,0,my(k=bigomega(n));numdiv(k>>valuation(k,2))) \\ Charles R Greathouse IV, Jul 29 2011