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

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

Offset: 1

Author

Joseph L. Pe, Jul 05 2002

Keywords

• base
• more
• nonn
• nice

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

Examples

			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.
		

Crossrefs

Cf. A001065, A004086, A069942.

Programs

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 *)

PARI

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

Extensions

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