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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

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OFFSET

1,1

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

Select[Range[90000], !PalindromeQ[#]&&DivisorSigma[1, #]==DivisorSigma[1, IntegerReverse[#]]&] (* Harvey P. Dale, Sep 09 2025 *)

PROG

(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

CROSSREFS

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

Sequence in context: A250754 A158364 A232885 * A157475 A373285 A158365

Adjacent sequences: A085326 A085327 A085328 * A085330 A085331 A085332

KEYWORD

base,nonn

AUTHOR

Labos Elemer, Jul 04 2003

STATUS

approved

URL: https://oeis.org/A085329

⇱ A085329 - OEIS