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 A066239 The floor(1.001*x)-perfect numbers, where f-perfect numbers for an arithmetical function f are defined in A066218. 0
 6, 28, 496, 32445, 130304, 388076, 199272950 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The floor(n)-perfect numbers are the ordinary perfect numbers. The first three floor[1.001x]-perfect numbers are also ordinary perfect numbers and the first discrepancy comes at the fourth term, 32445 (the fourth perfect number is 8128). Consider other coefficients > 1 but < 1.001. There is some kind of continuity working here. The first discrepancies, if they exist, come at later and later terms as these coefficients are made closer to 1. LINKS J. Pe, On a Generalization of Perfect Numbers, J. Rec. Math., 31(3) (2002-2003), 168-172. EXAMPLE Let f(n) = floor(1.001*n). Then f(6) = 6 = 3+2+1 = f(3)+f(2)+f(1); so 6 is a term of the sequence. MATHEMATICA f[x_] := Floor[1.001*x]; Select[ Range[1, 10^5], 2 * f[ # ] == Apply[ Plus, Map[ f, Divisors[ # ] ] ] & ] CROSSREFS Cf. A066218. Sequence in context: A060286 A000396 A152953 * A097464 A166998 A038182 Adjacent sequences:  A066236 A066237 A066238 * A066240 A066241 A066242 KEYWORD nonn,more AUTHOR Joseph L. Pe, Dec 19 2001 EXTENSIONS a(5)-a(7) from Amiram Eldar, Sep 26 2019 STATUS approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)