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A072228 Numbers n such that n = the sum of the reverses of the proper divisors of n. 2
6, 244, 285, 133857, 141635817, 273722772124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

I call these numbers "anti-perfect" (compare with the picture-perfect numbers A069942). These are all the anti-perfect numbers up to 3 * 10^6.

Next term is greater than 300000000. - Farideh Firoozbakht, Dec 23 2004

a(6) > 10^11. - Donovan Johnson, Dec 27 2013

a(7) > 10^12. - Giovanni Resta, Apr 07 2017

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

The proper divisors of 285 are 1, 3, 5, 15, 19, 57, 95, with sum of reverses = 1 + 3 + 5 + 51 + 91 + 75 + 59 =285. Therefore 285 is anti-perfect.

MATHEMATICA

f[n_] := FromDigits[Reverse[IntegerDigits[n]]]; Do[ If[n == Apply[Plus, Map[f, Drop[Divisors[n], -1]]], Print[n]], {n, 2, 10^7}]

Select[Range[15*10^7], Total[IntegerReverse[Most[Divisors[#]]]]==#&] (* Requires Mathematica version 10 or later *) (* The program takes a long time to run *) (* Harvey P. Dale, Aug 31 2016 *)

CROSSREFS

Cf. A069942, A101701.

Sequence in context: A156936 A231019 A254009 * A229631 A206307 A229475

Adjacent sequences:  A072225 A072226 A072227 * A072229 A072230 A072231

KEYWORD

base,more,nonn,nice

AUTHOR

Joseph L. Pe, Jul 05 2002

EXTENSIONS

One more term from Farideh Firoozbakht, Dec 23 2004

a(6) from Giovanni Resta, Apr 07 2017

STATUS

approved

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Last modified May 29 10:48 EDT 2017. Contains 287246 sequences.