login
A102749
Numbers k such that the largest prime-power dividing k is not a power of the largest prime dividing k.
2
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
1,1
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
LINKS
EXAMPLE
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.
MATHEMATICA
fQ[n_] := Block[{p = Power @@@ FactorInteger[n]}, Last[p] != Max[p]]; Select[Range[540], fQ] (* Ray Chandler, May 11 2007 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 09 2005
EXTENSIONS
More terms from Franklin T. Adams-Watters, Aug 29 2006
STATUS
approved