|
|
A106404
|
|
Number of even semiprimes dividing n.
|
|
5
|
|
|
0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,12
|
|
COMMENTS
|
Also the number of prime divisors p|n such that n/p is even. - Gus Wiseman, Jun 06 2018
|
|
LINKS
|
|
|
FORMULA
|
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)
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
(Haskell)
a106404 n = length [d | d <- takeWhile (<= n) a100484_list, mod n d == 0]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|