A102749 -id:A102749 - cp's OEIS frontend

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

Reinhard Zumkeller, Jun 22 2003

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

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

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

Cf. A006530, A020639, A028233, A053585, A085232, A363122.
A085233 is a subsequence.
Subsequence of A102749.

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

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

Edited by Peter Munn, Jun 01 2025

A126855 Numbers k such that, if k = product{p|k} p^c(k,p), each c(k,p) is a positive integer and each p is a distinct prime, then the smallest prime-power p^c(k, p) is not a power of the smallest prime dividing k.

Original entry on oeis.org

12, 24, 40, 45, 48, 56, 60, 63, 80, 84, 96, 112, 120, 132, 135, 144, 156, 160, 168, 175, 176, 189, 192, 204, 208, 224, 228, 240, 264, 275, 276, 280, 288, 297, 300, 312, 315, 320, 325, 336, 348, 351, 352, 360, 372, 384, 405, 408, 416, 420, 425, 440, 444, 448

Offset: 1

Leroy Quet, Mar 23 2007

nonn

The numbers of terms not exceeding 10^k, for k=1,2,...., are 0, 11, 128, 1245, 12474, 124052, 1240434, 12398594, 123976845, 1239840735, ... Apparently this sequence has an asymptotic density 0.1239... - Amiram Eldar, Mar 20 2021

			3600 is included because 3600 = 2^4 * 3^2 * 5^2 and the smallest prime-power (which is largest prime-power of its prime to divide 3600), 3^2 = 9, is not a power of the smallest prime to divide 3600, which is 2.

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

Cf. A020639, A034684, A102749.

fQ[n_] := Block[{p = Power @@@ FactorInteger[n]},First[p] != Min[p]];Select[Range[460], fQ] (* Ray Chandler, Mar 25 2007 *)

Extended by Ray Chandler, Mar 25 2007

cp's OEIS Frontend

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

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