A102749 Numbers k such that the largest prime-power dividing k is not a power of the largest prime dividing k.

12, 24, 40, 45, 48, 56, 63, 80, 90, 96, 112, 120, 126, 135, 144, 160, 168, 175, 176, 180, 189, 192, 208, 224, 240, 252, 270, 275, 280, 288, 297, 315, 320, 325, 336, 350, 351, 352, 360, 378, 384, 405, 416, 425, 448, 459, 475, 480, 504, 513, 525, 528, 539, 540

Offset: 1

Author

Leroy Quet, Feb 09 2005

Keywords

• nonn

Comments

Does this sequence have finite density? - Franklin T. Adams-Watters, Aug 29 2006

The numbers of terms not exceeding 10^k, for k=1,2,..., are 0, 10, 97, 706, 4779, 31249, 203799, 1322874, 8622492, 56559400, ... Apparently this sequence has an asymptotic density 0. - Amiram Eldar, Mar 20 2021

Examples

			45 is a term because 45 = 3^2*5 and 9 (the largest prime-power dividing 45) is not a power of 5 (the largest prime dividing 45).
144 is a term because its largest prime divisor is 3, but the largest prime power divisor, 16, is not a power of 3.
		

Links

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

Crossrefs

Cf. A006530, A034699, A126855.

Programs

Mathematica

fQ[n_] := Block[{p = Power @@@ FactorInteger[n]},Last[p] != Max[p]];Select[Range[540], fQ] (* Ray Chandler, May 11 2007 *)

Extensions

More terms from Franklin T. Adams-Watters, Aug 29 2006