A072413 Numbers k such that the LCM of exponents in the prime factorization of k does not equal the product of the exponents.

36, 100, 144, 180, 196, 216, 225, 252, 300, 324, 396, 400, 441, 450, 468, 484, 576, 588, 612, 676, 684, 700, 720, 784, 828, 882, 900, 980, 1000, 1008, 1044, 1080, 1089, 1100, 1116, 1156, 1200, 1225, 1260, 1296, 1300, 1332, 1444, 1452, 1476, 1512, 1521

Offset: 1

Author

Labos Elemer, Jun 17 2002

Keywords

• nonn

Comments

The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 2, 29, 348, 3548, 35761, 358258, 3583892, 35843109, 358440763, ... . Apparently, the asymptotic density of this sequence exists and equals 0.03584... . - Amiram Eldar, Sep 09 2022

Examples

			k = 36 = 2*2*3*3; exponent set = {2,2}; LCM = 2, product = 4.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005361, A051903, A051904, A052409, A052486, A072411-A072414.

Programs

Mathematica

Select[Range@ 1600, LCM @@ # != Times @@ # &@ Map[Last, FactorInteger@ #] &] (* Michael De Vlieger, May 15 2016 *)

PARI

is(n)=my(f=factor(n)[,2]); n>9 && lcm(f)!=factorback(f) \\ Charles R Greathouse IV, Jan 14 2017

Formula

A005361(a(n)) != A072411(a(n)).