|
|
A278478
|
|
a(n) is the 2-adic valuation of A000041(n).
|
|
9
|
|
|
0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 3, 0, 0, 0, 4, 0, 0, 0, 1, 0, 3, 1, 0, 0, 1, 2, 1, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 0, 2, 0, 1, 1, 6, 0, 0, 0, 5, 0, 0, 0, 2, 3, 0, 0, 2, 1, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 11, 1, 3, 0, 2, 1, 0, 1, 0, 0, 4, 0, 2, 7, 1, 0, 2, 2, 0, 0, 3, 2, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,12
|
|
COMMENTS
|
Write A000041(n) = 2^k * s where s is odd, then a(n) = k.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
a:= n-> padic[ordp](combinat[numbpart](n), 2):
|
|
MATHEMATICA
|
a[n_] := IntegerExponent[PartitionsP[n], 2]; Array[a, 100, 0] (* Amiram Eldar, May 25 2024 *)
|
|
PROG
|
(PARI) { my( x='x+O('x^100), v=Vec(1/eta(x)) ); vector(#v, n, valuation(v[n], 2)) }
|
|
CROSSREFS
|
Cf. A052002, A237280, A278779, A278780, A278781, A278782, A278783, A278784 (positions of terms 0, 1, 2, ..., 7 in this sequence).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|