

A072228


Numbers n such that n = the sum of the reverses of the proper divisors of n.


3




OFFSET

1,1


COMMENTS

I call these numbers "antiperfect" (compare with the pictureperfect numbers A069942). These are all the antiperfect 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 antiperfect.


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 * A322559 A229631 A206307
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



