A052202 Numbers k such that the product of the logarithms of k's prime factors is greater than their sum.

77, 85, 91, 95, 115, 119, 121, 133, 143, 145, 155, 161, 169, 185, 187, 203, 205, 209, 215, 217, 221, 235, 245, 247, 253, 259, 265, 275, 287, 289, 295, 299, 301, 305, 319, 323, 325, 329, 335, 341, 343, 355, 357, 361, 363, 365, 371, 377, 385, 391, 395, 399

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

Sequence in context: A344799 A344800 A294741 * A089525 A274172 A061671

Adjacent sequences: A052199 A052200 A052201 * A052203 A052204 A052205

Keyword

nonn

Author

Leroy Quet, Jan 28 2000

Extensions

Title changed by Charlie Neder, Dec 04 2018

Status

approved