A090315 Least k such that k and digit reversal of k both have n divisors, or 0 if no such number exists.

1, 2, 4, 6, 14641, 44, 0, 24, 484, 272, 0, 294, 0, 291008, 44944, 264, 0, 252, 0, 2992, 0, 2532352, 0, 2508, 10004000600040001, 2977792, 1002001, 2112, 0, 63536, 0, 4224, 0, 44356665344, 0, 2772, 0, 2380651036672, 0, 42224, 0, 6336, 0, 2937856, 698896, 0

Offset

1,2

Comments

For a(7) one needs a number of the form p^6 whose digit reversal is q^6, p, q are primes. Hence a(7) perhaps is zero (not sure). Conjecture: There are infinitely many nonzero terms as well as zeros in this sequence.

Zeros are unproved. I have checked for a(21) up to 10^13, a(46) up to 10^14, a(33) up to 10^18, a(39) up to 10^20, a(35) up to 10^30 and the rest (7, 11, 13, 17, 19, 23, 29, 31, 37, 41 and 43) up to at least 10^48. - David Wasserman, Nov 01 2005

Links

Table of n, a(n) for n=1..46.

Example

a(8) =24, tau(24) = tau(42) = 8.

Crossrefs

Cf. A083753.

Sequence in context: A033319 A185151 A218087 * A083753 A170807 A221840

Adjacent sequences: A090312 A090313 A090314 * A090316 A090317 A090318

Keyword

base,nonn

Author

Amarnath Murthy, Dec 01 2003

Extensions

More terms from David Wasserman, Nov 01 2005

Status

approved