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

1,2

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

Links

Table of n, a(n) for n=1..45.

Crossrefs

Cf. A002113, A076888.

Sequence in context: A185151 A218087 A090315 * A170807 A221840 A111512

Adjacent sequences: A083750 A083751 A083752 * A083754 A083755 A083756

Keyword

base,nonn

Author

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

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

Status

approved