A193510 Number of even divisors of Omega(n).

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

Offset

1,16

Comments

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

Records are at 4^A002182(n). [Charles R Greathouse IV, Jul 29 2011]

Links

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

Example

a(16) = 2 because Omega(16) = 4 and the 2 even divisors are {2, 4}.

Mathematica

f[n_] := Block[{d = Divisors[PrimeOmega[n]]}, Count[EvenQ[d], True]]; Table[f[n], {n, 80}]
Join[{0}, Table[Count[Divisors[PrimeOmega[n]], _?EvenQ], {n, 2, 100}]] (* Harvey P. Dale, Jul 05 2023 *)

Prog

(PARI) a(n)=my(k=bigomega(n)); if(!k||k%2, 0, numdiv(k/2)) \\ Charles R Greathouse IV, Jul 29 2011

Crossrefs

Cf. A183063, A001222, A193509.

Sequence in context: A266344 A334944 A174875 * A353337 A351907 A357374

Adjacent sequences: A193507 A193508 A193509 * A193511 A193512 A193513

Keyword

nonn

Author

Michel Lagneau, Jul 29 2011

Status

approved