A093036 Number of palindromic divisors of a(n) sets a new record.

1, 2, 4, 6, 12, 24, 66, 132, 264, 792, 1848, 2772, 5544, 13332, 14652, 24024, 26664, 72072, 79992, 186648, 205128, 264264, 559944, 792792, 1333332, 2666664, 7279272, 7999992, 13333320, 14666652, 26690664, 29333304, 80071992, 134666532, 269333064, 807999192

Offset

1,2

Comments

Beginning with 132, it appears that all entries are congruent mod 11*12; 11 to produce palindromic divisors and 12 for numerous divisors. - Robert G. Wilson v, May 14 2004

The number of palindromic divisors of a(n) are 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 16, 19, 20, 21, 22, 24, 27, 28, 29, 30, 33, 37, 39, 43, 50, 52, 54, 57, 59, 61, 68, 72, 80, 90.

Every term is of the form Product_{i>=1} A226732(i)^e(i) for e(i) >= 0. - David A. Corneth, Jan 10 2021

References

Jason Earls, "Palindions," Mathematical Bliss, Pleroma Publications, 2009, pages 115-120. ASIN: B002ACVZ6O. [From Jason Earls, Nov 25 2009]

Links

Table of n, a(n) for n=1..36.

David A. Corneth, Conjectured next terms

Mathematica

palindromicQ[n_, b_:10] := If[FromDigits[Reverse[IntegerDigits[n, b]], b] == n, True, False]; a = 0; Do[c = Count[palindromicQ[ # ] & /@ Divisors[n], True]; If[c > a, Print[n]; a = c], {n, 300000000}] (* Robert G. Wilson v, May 14 2004 with a small modification from Alonso del Arte to permit reuse in many other sequences' programs *)

Crossrefs

Cf. A087990, A002093, A226732.

Sequence in context: A036484 A212654 A337993 * A340548 A087997 A355699

Adjacent sequences: A093033 A093034 A093035 * A093037 A093038 A093039

Keyword

nonn,base

Author

Jason Earls, May 08 2004

Extensions

Edited and extended by Robert G. Wilson v, May 14 2004

a(35)-a(36) from Chai Wah Wu, Jan 21 2021

Status

approved