OFFSET

1,1

COMMENTS

First even term is 1334.

Previous name was: If p^a(p,n) is highest power of p that divides n, then Product_(p=primes) [log(p)^a(p,n) ] > log(n).

From Charlie Neder, Dec 03 2018: (Start)

Primes are counted with multiplicity.

Does this sequence have asymptotic density 1?

a(100000) = 189835. (End)

LINKS

Charlie Neder, Table of n, a(n) for n = 1..1000

EXAMPLE

245 is included because 245 = 5*7^2 and log(5)*log(7)^2 > log(245).

MATHEMATICA

aQ[n_] := Times@@Power@@@({Log[#1], #2} & @@@FactorInteger[n]) > Log[n]; Select[Range[400], aQ] (* Amiram Eldar, Dec 03 2018 *)

PROG

(PARI) isok(n) = my(f=factor(n)); prod(k=1, #f~, log(f[k, 1])^f[k, 2]) > log(n); \\ Michel Marcus, Dec 04 2018

CROSSREFS

KEYWORD

nonn

AUTHOR

Leroy Quet, Jan 28 2000

EXTENSIONS

Title changed by Charlie Neder, Dec 04 2018

STATUS

approved