A083753 Smallest palindromic number with exactly n divisors, or 0 if no such number exists.

1, 2, 4, 6, 14641, 44, 0, 66, 484, 272, 0, 414, 0, 2912192, 44944, 616, 0, 252, 0, 2992, 0, 2532352, 0, 4004, 10004000600040001, 2977792, 1002001, 2112, 0, 63536, 0, 4224, 0, 44356665344, 0, 2772, 0, 6564989894656, 0, 42224, 0, 6336, 0, 4015104, 698896

Offset: 1

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003

Keywords

• base
• nonn

Comments

a(7)=a(11)=a(13)=a(17)=a(19)=a(23)=a(29)=a(31)=a(37)=a(41)=0 under the plausible conjecture that there are no palindromes > 1 which are fifth or higher powers. David Wasserman in A090315 reports that he has checked this (or rather the part needed for this sequence) up to 10^48. - David Consiglio, Jr. and Charles R Greathouse IV, Mar 27 2012

a(21), a(33), a(35), and a(39) have also not been proved to be zero, but if positive they must be at least 10^31. - Charles R Greathouse IV, Mar 27 2012

Crossrefs

Cf. A002113, A076888.

Extensions

a(11)-a(42) from David Consiglio, Jr. and Charles R Greathouse IV, Mar 27 2012

a(43)-a(45) added (with a(43)=0 under the same conjecture as for a(7)=a(11)=...=a(41)=0) by Jon E. Schoenfield, Oct 17 2014