|
| |
|
|
A373155
|
|
a(n) = 1 if n is a non-multiple of 3 whose 2-adic valuation is even, otherwise 0.
|
|
2
|
|
|
|
1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1
|
|
|
LINKS
|
|
|
|
FORMULA
|
Multiplicative with a(2^e) = 1 if e is even, 0 if e is odd, a(3^e) = 0, and a(p^e) = 1 for any prime p > 3.
Dirichlet g.f.: (2^s/(2^s+1)) * (1-1/3^s) * zeta(s).
Sum_{k=1..n} a(k) ~ (4/9) * n. (End)
|
|
|
MATHEMATICA
|
a[n_] := If[EvenQ[IntegerExponent[n, 2]] && !Divisible[n, 3], 1, 0]; Array[a, 100] (* Amiram Eldar, May 29 2024 *)
|
|
|
PROG
|
(PARI) A373155(n) = ((n%3) && !(valuation(n, 2)%2));
(PARI) A373155(n) = { my(f = factor(n)); prod(k=1, #f~, if(2==f[k, 1], !(f[k, 2]%2), f[k, 1] > 3)); };
|
|
|
CROSSREFS
|
Characteristic function of A084087.
Absolute values and also parity of A084091.
|
|
|
KEYWORD
|
nonn,mult,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
