A375667 The maximum exponent in the prime factorization of the 5-rough numbers (A007310).

0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,9

Links

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

Formula

a(n) = A051903(A007310(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - 1/((1-1/2^k) * (1-1/3^k) * zeta(k))) = 1.1034178389191320571029... .

Mathematica

a[n_] := Max[FactorInteger[6*Floor[n/2] - (-1)^n][[;; , 2]]]; a[1] = 0; Array[a, 100]

Prog

(PARI) a(n) = if(n == 1, 0, vecmax(factor(n\2*6-(-1)^n)[, 2]));

Crossrefs

Cf. A007310, A051903, A375039, A375668.

Sequence in context: A136713 A224782 A160322 * A341644 A198293 A368330

Adjacent sequences: A375664 A375665 A375666 * A375668 A375669 A375670

Keyword

nonn,easy

Author

Amiram Eldar, Aug 23 2024

Status

approved