A085231 Numbers k in whose canonical factorization the power of the smallest prime factor is greater than the power of the greatest prime factor.

12, 24, 40, 45, 48, 56, 63, 80, 96, 112, 120, 135, 144, 160, 168, 175, 176, 189, 192, 208, 224, 240, 275, 280, 288, 297, 315, 320, 325, 336, 351, 352, 360, 384, 405, 416, 425, 448, 459, 475, 480, 504, 513, 528, 539, 544, 560, 567, 575, 576, 608, 621, 624

Offset: 1

Author

Reinhard Zumkeller, Jun 22 2003

Keywords

• nonn
• easy

Comments

p*a(n) is a term for all primes p with A020639(a(n)) < p < A006530(a(n)).

Examples

			The canonical factorization of 240 is 2^4 * 3 * 5. 2^4 = 16 > 5, therefore 240 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006530, A020639, A028233, A053585, A085232, A363122.

A085233 is a subsequence.

Subsequence of A102749.

Programs

Mathematica

pfgQ[n_]:=Module[{fe=#[[1]]^#[[2]]&/@FactorInteger[n]},fe[[1]]>fe[[-1]]]; Select[Range[700],pfgQ] (* Harvey P. Dale, Dec 11 2017 *)

Formula

A028233(a(n)) > A053585(a(n)).

Extensions

Edited by Peter Munn, Jun 01 2025