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

Author

Jason Earls, May 08 2004

Keywords

• nonn
• base

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

• David A. Corneth, Conjectured next terms

Crossrefs

Cf. A087990, A002093, A226732.

Programs

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 *)

Extensions

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

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