A085329 Non-palindromic solutions to sigma(R(n)) = sigma(n), where R = A004086 is digit-reversal.

528, 825, 1561, 1651, 4064, 4604, 5346, 5795, 5975, 6435, 15092, 15732, 21252, 23751, 25212, 29051, 34536, 38115, 39325, 39516, 51183, 52393, 53295, 53768, 59235, 61593, 63543, 64328, 69368, 70577, 77507, 81558, 82346, 85518, 86396

Offset: 1

Author

Labos Elemer, Jul 04 2003

Keywords

• base
• nonn

Comments

Without the non-palindromic condition, the first 62 terms would be identical to the list of palindromes A002113. - M. F. Hasler, May 13 2025

Examples

			sigma(528) = sigma(825) = 1488.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203 (sigma), A004086 (R), A350867 (similar with d = sigma_0).

Programs

Mathematica

nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] red[x_] := Reverse[IntegerDigits[x]] Do[s=DivisorSigma[1, n]; s1=DivisorSigma[1, tn[red[n]]]; If[Equal[s, s1]&&!Equal[n, tn[red[n]]], Print[{n, s}]], {n, 1, 1000000}]
srnQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn];idn!=ridn && DivisorSigma[1,n]==DivisorSigma[1,FromDigits[ridn]]]; Select[Range[ 100000], srnQ] (* Harvey P. Dale, Oct 25 2011 *)

PARI

select( {is_A085329(n, r=A004086(n))=sigma(n)==sigma(r)&&n!=r}, [1..50000]) \\ M. F. Hasler, May 13 2025

Python

from sympy import divisor_sigma as sigma
def is_A085329(n): return sigma(n)==sigma(r:=int(str(n)[::-1])) and n!=r # M. F. Hasler, May 13 2025

Formula

Solutions to (A000203(x) = A000203(A004086(x)) and A004086(x) <> x).