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

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

Examples

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

Links

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

Crossrefs

Cf. A183063, A001222, A193509.

Programs

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 *)

PARI

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