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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Crossrefs

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

A085233 is a subsequence.

Subsequence of A102749.

Sequence in context: A140831 A126855 A102749 * A057715 A357863 A053990

Adjacent sequences: A085228 A085229 A085230 * A085232 A085233 A085234

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jun 22 2003

Extensions

Edited by Peter Munn, Jun 01 2025

Status

approved