A072234 Numbers k such that reverse(k) = sum of the proper divisors of k.

6, 498906, 20671542, 41673714, 73687923, 4158499614, 922964834547

Offset

1,1

Comments

Mark Ganson conjectures that all terms are divisible by 3.

Jens Kruse Andersen discovered that 4158499614 is in the sequence (although he did not rule out the possibility that there were missing terms below this - that was established by Giovanni Resta).

a(8) > 10^13. - Giovanni Resta, Dec 12 2013

Links

Table of n, a(n) for n=1..7.

Example

The proper divisors of 498906 are 1, 2, 3, 6, 9, 18, 27, 54, 9239, 18478, 27717, 55434, 83151, 166302, 249453, which sum to 609894, the reverse of 498906; hence 498906 is a term of the sequence.

Mathematica

f = IntegerReverse; Do[ If[f[n] == Apply[Plus, Drop[Divisors[n], -1]], Print[n]], {n, 2, 10^9}]
Select[Range[500000], IntegerReverse[#]==Total[Most[Divisors[#]]]&] (* The program generates the first 2 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Dec 30 2024 *)

Prog

(PARI) for(n=1, 10^9, if(sigma(n)-n==eval(concat(Vecrev(Str(n)))), print1(n, ", "))) \\ Edward Jiang, Sep 10 2014

Crossrefs

Cf. A001065, A004086, A069942.

Sequence in context: A238821 A067503 A079288 * A369973 A172823 A182791

Adjacent sequences: A072231 A072232 A072233 * A072235 A072236 A072237

Keyword

base,more,nonn,nice

Author

Joseph L. Pe, Jul 05 2002

Extensions

a(6) confirmed and a(7) discovered by Giovanni Resta, Dec 12 2013

Status

approved