A072412 Numbers k such that the LCM of exponents in the prime factorization of k does not equal the largest exponent.

72, 108, 200, 288, 360, 392, 432, 500, 504, 540, 600, 648, 675, 756, 792, 800, 864, 936, 968, 972, 1125, 1152, 1176, 1188, 1224, 1323, 1350, 1352, 1368, 1372, 1400, 1404, 1440, 1500, 1568, 1656, 1800, 1836, 1944, 1960, 2000, 2016, 2052, 2088, 2160

Offset: 1

Author

Labos Elemer, Jun 17 2002

Keywords

• nonn

Comments

This sequence differs from the Achilles numbers (A052486).

Examples

			k = 360 = 2*2*2*3*3*5, exponent set = {3,2,1}; LCM=6, max=3.
		

Links

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

Crossrefs

Cf. A005361, A051903, A051904, A052409, A052486, A072411, A072413, A072414.

Programs

Mathematica

Select[Range[2000], LCM @@ (e = FactorInteger[#][[;; , 2]]) != Max[e] &] (* Amiram Eldar, Jul 30 2022 *)

PARI

is(n)=my(f=factor(n)[,2]); n>9 && vecmax(f)!=lcm(f) \\ Charles R Greathouse IV, Oct 16 2015

Formula

A051903(a(n)) != A072411(a(n)).