A375668 The maximum exponent in the prime factorization of the 7-rough numbers (A007775).

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

Offset

1,14

Links

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

Formula

a(n) = A051903(A007775(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) * (1-1/5^k) * zeta(k))) = 1.05546104674564363968... .

In general, the asymptotic mean of the maximum exponent in the prime factorization of the p-rough numbers (numbers that are not divisible by any prime smaller than p) is 1 + Sum_{k>=2} (1 - 1/(zeta(k) * Product_{primes q < p} (1-1/q^k))).

Mathematica

If[# == 1, 0, Max[FactorInteger[#][[;; , 2]]]] & /@ Select[Range[300], CoprimeQ[#, 30] &]

Prog

(PARI) lista(nmax) = print1(0, ", "); for(n = 2, nmax, if(gcd(n, 30) == 1, print1(vecmax(factor(n)[, 2]), ", ")));

Crossrefs

Cf. A007775, A051903, A375039, A375667.

Sequence in context: A318829 A113515 A103754 * A058665 A327103 A290105

Adjacent sequences: A375665 A375666 A375667 * A375669 A375670 A375671

Keyword

nonn,easy

Author

Amiram Eldar, Aug 23 2024

Status

approved