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

1,8

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]

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001222.

Sequence in context: A338274 A210960 A339095 * A331284 A331591 A003649

Adjacent sequences: A193506 A193507 A193508 * A193510 A193511 A193512

Keyword

nonn

Author

Michel Lagneau, Jul 29 2011

Status

approved