OFFSET
1,15
COMMENTS
Equivalently, a(n) is the number of prime divisors p|n such that n/p is odd. - Gus Wiseman, Jun 06 2018
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
O.g.f.: Sum_{p prime} x^p/(1 - x^(2p)). - Gus Wiseman, Jun 06 2018
Sum_{k=1..n} a(k) = (n/2) * (log(log(n)) + B) + O(n/log(n)), where B is Mertens's constant (A077761). - Amiram Eldar, Sep 21 2024
MATHEMATICA
a[n_] := Sum[ Boole[ OddQ[d] && PrimeQ[n/d] ], {d, Divisors[n]} ]; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 27 2013 *)
PROG
(Sage)
def A205745(n):
return sum((n//d) % 2 for d in divisors(n) if is_prime(d))
[A205745(n) for n in (1..105)]
(PARI) a(n)=if(n%2, omega(n), n%4/2) \\ Charles R Greathouse IV, Jan 30 2012
(Haskell)
a205745 n = sum $ map ((`mod` 2) . (n `div`))
[p | p <- takeWhile (<= n) a000040_list, n `mod` p == 0]
-- Reinhard Zumkeller, Jan 31 2012
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Peter Luschny, Jan 30 2012
STATUS
approved