A070844 a(n) = smallest n-digit number with exactly n divisors, or 0 if no such number exists.

1, 11, 121, 1003, 14641, 100017, 1771561, 10000005, 100020001, 1000000016, 25937424601, 100000000004, 3138428376721, 10000000001344, 100000720001296, 1000000000000006, 45949729863572161, 100000000000000404

Offset: 1

Author

Amarnath Murthy, May 12 2002

Keywords

• base
• nonn

Links

• Ray Chandler, Table of n, a(n) for n=1..41

Crossrefs

Cf. A070845.

Programs

Mathematica

For[n=1, n<10, n++, k := 10^(n-1); While[Not[Length[Divisors[k]] == n], k++ ]; Print[k]] (Steinerberger)

Formula

If n is a prime < 29 then a(n) = 11^(n-1). - Chandler

If n is a prime >= 29 then a(n) = 0. - Vladeta Jovovic, Aug 20 2002

Extensions

a(6)-a(18) from Vladeta Jovovic, Aug 20 2002

a(6) confirmed by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 08 2003

a(7)-a(10) confirmed by Stefan Steinerberger, Feb 06 2006

a(15) corrected, and a(11)-a(14), a(16)-a(18) confirmed by Ray Chandler, Feb 10 2009

Edited by N. J. A. Sloane, Feb 14 2009 at the suggestion of Ray Chandler.