A380802 a(n) = log_2(A053026(n)).

0, 1, 2, 3, 4, 3, 2, 2, 2, 4, 3, 3, 3, 3, 3, 1, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 4, 2, 4, 3, 4, 2, 2, 4, 2, 2, 1, 2, 4, 3, 4, 4, 2, 3, 3, 2, 3, 3, 4, 3, 3, 5, 5, 2, 5, 2, 2, 3, 2, 1, 5, 1, 3, 2, 3, 2, 3, 3, 3, 3, 1, 3, 3, 3, 5, 5, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 5, 3, 3, 1, 2, 1, 2, 3, 2, 2, 3, 3, 1, 3, 5, 2, 3, 2

Offset: 1

Author

Amiram Eldar, Feb 04 2025

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053026, A380803.

Programs

Mathematica

a[n_] := Log2[NestWhile[DivisorSigma[0, #] &, n!, # != 2^IntegerExponent[#, 2] &]]; Array[a, 100]

PARI

a(n) = {my(m = n!); while(1 << valuation(m, 2) != m, m = numdiv(m)); valuation(m, 2);}