A062687 -id:A062687 - cp's OEIS frontend

A340252 Numbers whose pairwise products of divisors are all palindromic.

1, 2, 3, 4, 5, 7, 11, 22, 33, 101, 121, 131, 151, 181, 191, 202, 303, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 1111, 2222, 10201, 10301, 10501, 10601, 11311, 11411, 12221, 12421, 12721, 12821, 13331, 13831, 13931, 14341, 14741, 15451, 15551, 16061, 16361, 16561, 16661

Offset: 1

Ivan N. Ianakiev, Jan 02 2021

Supersequence of A002385 (palindromic primes).

A subsequence of A062687 (numbers all of whose divisors are palindromic).

			The pairwise products of the divisors of 22 (2,11,22,44,242) are all palindromic, so 22 is in the sequence.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A002385, A062687.

fQ[n_]:=AllTrue[Union[Times@@@Subsets[Divisors[n],{2}]],PalindromeQ]; Select[Range[20000],fQ]

A084981 Numbers all of whose proper divisors are palindromic.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 25, 27, 29, 31, 33, 35, 37, 41, 43, 44, 47, 49, 53, 55, 59, 61, 66, 67, 71, 73, 77, 79, 83, 88, 89, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179

Offset: 1

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 27 2003

77566 is in the sequence because its proper divisors are: 1, 2, 38783.

Cf. A062687.

Edited by Jason Earls, May 13 2004

A192219 Numbers m such that set of divisors of m is equal to set of reversals of divisors of m but all divisors of m are not palindromic.

Original entry on oeis.org

1226221, 13488431, 123848321, 12467976421, 1030507050301, 1120237320211, 1225559555221, 1234469644321, 1334459544331, 11335577553311, 100330272033001, 101222252222101, 103023070320301, 113143969341311, 121363494363121, 134312696213431

Offset: 1

Jaroslav Krizek, Jul 13 2011

All terms are palindromic (subsequence of A002113 - palindromic numbers).
Subsequence of A188650 (numbers that are divisible by all reversals of their divisors).
Union a(n) and A062687 (numbers all of whose divisors are palindromic) is sequence of numbers m such that set of divisors of m is equal to set of reversals of divisors of m: {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 121, 131, ..., 1226221, ...}. - Jaroslav Krizek, Jul 18 2011

			1226221 has divisors 1, 1021, 1201, 1226221. Set of divisors is equal to set of reversals of divisors. Divisors 1021 and 1201 are not palindromic.

t = Union[Flatten[Table[d = IntegerDigits[n]; {FromDigits[Join[d, Reverse[d]]], FromDigits[Join[d, Reverse[Most[d]]]]}, {n, 0, 99999}]]]; okQ[n_] := Module[{f = Divisors[n], r}, r = f; Do[r[[i]] = FromDigits[Reverse[IntegerDigits[f[[i]]]]], {i, Length[f]}];  f == Sort[r] && f != r]; Select[t, okQ] (* T. D. Noe, Jul 14 2011 *)

a(5)-a(16) (including six found by T. D. Noe) from Donovan Johnson, Jul 14 2011

A326929 Numbers whose divisors and arithmetic mean of divisors are palindromic.

Original entry on oeis.org

1, 3, 5, 6, 7, 11, 22, 131, 262, 13331, 26662, 1333331, 2666662

Offset: 1

Ivan N. Ianakiev, Oct 22 2019

a(14) is greater than 10^18 and at most (10^94-1)*(4/3)-1. - Charles R Greathouse IV, Oct 28 2019

(4*10^A259050(n)-7)/3 and (8*10^A259050(n)-14)/3 are terms. Conjecture: all terms > 10 are of these forms. - Chai Wah Wu, Nov 17 2019

			The divisors of 2666662 are {1,2,1333331,2666662} which are all palindromic. Their arithmetic mean is 999999 and is also palindromic. Therefore, 2666662 is in the sequence.

Subsequence of A062687 and hence of A002113.
Subsequence of A003601.
Cf. A259050.

palQ[n_]:=ToString[n]==StringReverse[ToString[n]];
fQ[n_]:=palQ[Mean[Divisors[n]]]&&Union[palQ/@Divisors[n]]=={True};
Select[Range[2666662],fQ]

cp's OEIS Frontend

A340252 Numbers whose pairwise products of divisors are all palindromic.

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A084981 Numbers all of whose proper divisors are palindromic.

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A192219 Numbers m such that set of divisors of m is equal to set of reversals of divisors of m but all divisors of m are not palindromic.

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A326929 Numbers whose divisors and arithmetic mean of divisors are palindromic.

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