A350867 -id:A350867 - cp's OEIS frontend

A062895 Numbers k for which d(k) = d(R(k)), where R(k) is the reversal of k and d(k) is the number of divisors of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 22, 24, 26, 31, 33, 37, 39, 42, 44, 51, 55, 58, 62, 66, 71, 73, 77, 79, 85, 88, 93, 97, 99, 101, 107, 111, 113, 115, 117, 121, 122, 123, 129, 131, 141, 143, 149, 151, 155, 157, 158, 159, 161, 165, 167, 169, 171, 177, 178, 179

Offset: 1

Amarnath Murthy, Jun 30 2001

The sequence s of numbers k for which R(d(k)) = d(R(k)) first differs at s(80) = 262 while a(80) = 252. - Mohammed Yaseen, Mar 24 2023

			d(24) = 8 and also d(42) = 8, hence both are members.

Mohammed Yaseen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Cf. A000005 (d), A004086 (R), A002113 (palindromes: subsequence).

Cf. A350867 (subsequence of non-palindromic terms), A085329 (similar with sigma).

Select[Range[180],DivisorSigma[0,#]==DivisorSigma[0,FromDigits[Reverse[IntegerDigits[#]]]] &] (* Jayanta Basu, May 17 2013 *)

{ n=0; for (m=1, 10^9, x=m; r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); if (numdiv(m) == numdiv(r), write("b062895.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 12 2009

isok(k) = numdiv(fromdigits(Vecrev(digits(k)))) == numdiv(k); \\ Michel Marcus, Jul 06 2021

from sympy import divisor_count as d
def ok(n): return d(n) == d(int(str(n)[::-1]))
print([k for k in range(1, 180) if ok(k)]) # Michael S. Branicky, Mar 24 2023

Corrected and extended by Vladeta Jovovic, Jun 30 2001

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

Original entry on oeis.org

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

Labos Elemer, Jul 04 2003

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

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

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

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

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

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

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

A354745 Non-repdigit numbers k such that every permutation of the digits of k has the same number of divisors.

Original entry on oeis.org

13, 15, 17, 24, 26, 31, 37, 39, 42, 51, 58, 62, 71, 73, 79, 85, 93, 97, 113, 117, 131, 155, 171, 177, 178, 187, 199, 226, 262, 288, 311, 337, 339, 355, 373, 393, 515, 535, 551, 553, 558, 585, 622, 711, 717, 718, 733, 771, 781, 817, 828, 855, 871, 882, 899, 919, 933, 989, 991, 998

Offset: 1

Metin Sariyar, Jun 05 2022

After a(93) = 84444, no further terms < 10^18. - Michael S. Branicky, Jun 08 2022

			871 is a term because d(871) = d(817) = d(178) = d(187) = d(718) = d(781) = 4, where d(n) is the number of divisors of n.

Cf. A000005, A003459, A067012, A062895, A350867, A354746.

Select[Range[10000],CountDistinct[DivisorSigma[0,FromDigits /@ Permutations[IntegerDigits[#]]]]==1&&CountDistinct[IntegerDigits[#]]>1&]

from sympy import divisor_count
from itertools import permutations
def ok(n):
    s, d = str(n), divisor_count(n)
    if len(set(s)) == 1: return False
    return all(d==divisor_count(int("".join(p))) for p in permutations(s))
print([k for k in range(5500) if ok(k)]) # Michael S. Branicky, Jun 05 2022

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A062895 Numbers k for which d(k) = d(R(k)), where R(k) is the reversal of k and d(k) is the number of divisors of k.

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

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A354745 Non-repdigit numbers k such that every permutation of the digits of k has the same number of divisors.

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Python