A086291 Maximal exponent in prime factorization of 7-smooth numbers.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 1, 4, 2, 2, 1, 3, 2, 3, 2, 1, 5, 1, 2, 3, 1, 2, 4, 2, 2, 3, 3, 2, 2, 6, 1, 3, 2, 4, 4, 2, 2, 5, 2, 2, 1, 3, 4, 3, 3, 2, 7, 3, 2, 4, 2, 2, 5, 4, 3, 2, 2, 3, 6, 2, 3, 1, 3, 5, 2, 4, 5, 2, 3, 2, 8, 3, 3, 5, 2, 2, 2, 6, 4, 4, 3, 2, 3, 3, 3, 7, 3, 4, 4, 2, 4, 2, 6, 2

Offset: 1

Author

Reinhard Zumkeller, Jul 15 2003

Keywords

• nonn

Links

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

Crossrefs

Cf. A002473, A051903, A086289, A086290.

Programs

Mathematica

maxExp[1] = 0; maxExp[n_] := Max @@ Last /@ FactorInteger[n]; maxExp/@Select[Range[500], Max[Transpose[FactorInteger[#]][[1]]] <= 7 &] (* Amiram Eldar, Jan 06 2020 *)

Formula

a(n) = A051903(A002473(n)).

A086290(n) <= a(n) <= A086289(n).