A102749 - OEIS

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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

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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

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

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

Cf. A006530, A034699, A126855.

Sequence in context: A139406 A140831 A126855 * A085231 A057715 A357863

Adjacent sequences: A102746 A102747 A102748 * A102750 A102751 A102752

KEYWORD

nonn

AUTHOR

Leroy Quet, Feb 09 2005

EXTENSIONS

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

STATUS

approved