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

1,1

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A114819 A137945 A250812 * A131605 A376119 A296204

Adjacent sequences: A072410 A072411 A072412 * A072414 A072415 A072416

Keyword

nonn

Author

Labos Elemer, Jun 17 2002

Status

approved