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 A069266 Numbers k such that Sum_{d|k} d/core(d) > 2*k, where core(d) is the squarefree part of d. 1
 576, 1296, 2304, 3600, 5184, 7056, 8100, 9216, 11664, 14400, 17424, 20736, 24336, 28224, 32400, 36864, 44100, 46656, 57600, 63504, 69696, 72900, 82944, 90000, 97344, 104976, 108900, 112896, 129600, 147456, 152100, 156816, 166464, 176400, 186624, 202500, 207936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms <= 10^17 are squares. Are there any nonsquare terms? - David A. Corneth, Sep 05 2020 LINKS David A. Corneth, Table of n, a(n) for n = 1..10000 (first 5000 terms from Amiram Eldar) FORMULA Numbers k such that A068976(k) > 2*k. EXAMPLE 3600 is in the sequence as its divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, ..., 400, 450, 600, 720, 900, 1200, 1800, 3600 and the respective values d/core(d) are 1, 1, 1, 4, 1, 1, 4, 9, ... , 900, 400, 900, 3600. The sum of this latter list is 7722 which is greater than 2*3600. - David A. Corneth, Sep 05 2020 MATHEMATICA f[p_, e_] := If[OddQ[e], 2*(p^(e + 1) - 1)/(p^2 - 1), (p^(e + 2) + p^e - 2)/(p^2 - 1)]; Select[Range[2, 150000], Times @@ (f @@@ FactorInteger[#]) > 2*# &] (* Amiram Eldar, Sep 05 2020 *) PROG is(n) = sumdiv(n, d, d/core(d)) > n << 1 \\ David A. Corneth, Sep 05 2020 CROSSREFS Cf. A068976, A007913. Sequence in context: A109101 A258919 A064253 * A060678 A254848 A235181 Adjacent sequences:  A069263 A069264 A069265 * A069267 A069268 A069269 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Apr 14 2002 EXTENSIONS More terms from Amiram Eldar, Sep 05 2020 STATUS approved

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Last modified May 28 00:30 EDT 2022. Contains 354110 sequences. (Running on oeis4.)