OFFSET
1,12
COMMENTS
Also the number of prime divisors p|n such that n/p is even. - Gus Wiseman, Jun 06 2018
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(A100484(n)) = 1.
a(A005408(n)) = 0.
a(A005843(n)) > 0 for n>1.
a(2n) = omega(n), a(2n+1) = 0, where omega(n) is the number of distinct prime divisors of n, A001221. - Franklin T. Adams-Watters, Jun 09 2006
a(n) = card { d | d*p = n, d even, p prime }. - Peter Luschny, Jan 30 2012
O.g.f.: Sum_{p prime} x^(2p)/(1 - x^(2p)). - Gus Wiseman, Jun 06 2018
EXAMPLE
a(60) = #{4, 6, 10} = #{2*2, 2*3, 2*5} = 3.
MATHEMATICA
Table[Length[Select[Divisors[n], PrimeQ[#]&&EvenQ[n/#]&]], {n, 100}] (* Gus Wiseman, Jun 06 2018 *)
Table[Count[Divisors[n], _?(EvenQ[#]&&PrimeOmega[#]==2&)], {n, 110}] (* Harvey P. Dale, May 04 2021 *)
a[n_] := If[EvenQ[n], PrimeNu[n/2], 0]; Array[a, 100] (* Amiram Eldar, Jun 26 2022 *)
PROG
(Sage)
def A106404(n):
return add(1-(n/d)%2 for d in divisors(n) if is_prime(d))
print([A106404(n) for n in (1..105)]) # Peter Luschny, Jan 30 2012
(PARI) a(n)=if(n%2, 0, omega(n/2)) \\ Charles R Greathouse IV, Jan 30 2012
(Haskell)
a106404 n = length [d | d <- takeWhile (<= n) a100484_list, mod n d == 0]
-- Reinhard Zumkeller, Jan 31 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 02 2005
STATUS
approved