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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
OFFSET
0,12
COMMENTS
Write A000041(n) = 2^k * s where s is odd, then a(n) = k.
FORMULA
From Amiram Eldar, May 25 2024: (Start)
a(n) = A007814(A000041(n)).
a(n) = log_2(A069935(n). (End)
MAPLE
a:= n-> padic[ordp](combinat[numbpart](n), 2):
seq(a(n), n=0..120); # Alois P. Heinz, Nov 23 2016
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).
Cf. also A278241.
Sequence in context: A267502 A296605 A354488 * A364107 A122480 A096133
KEYWORD
nonn
AUTHOR
Joerg Arndt, Nov 23 2016
STATUS
approved