A182680 a(n) = the largest n-digit number with exactly 10 divisors, a(n) = 0 if no such number exists.

0, 80, 976, 9904, 99952, 999952, 9999952, 99999824, 999999536, 9999999824, 99999999536, 999999999567, 9999999999963, 99999999999728, 999999999999856, 9999999999998896, 99999999999999824, 999999999999999952, 9999999999999999856, 99999999999999999568

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• base

Comments

a(n) = the largest n-digit number of the form p^9 or p^4*q (p, q distinct primes), a(n) = 0 if no such number exists.

Crossrefs

Cf. A030628, A182679.

Programs

Mathematica

Table[k=10^n-1; While[k>10^(n-1) && DivisorSigma[0, k] != 10, k--]; If[k==10^(n-1), k=0]; k, {n, 20}]

Formula

A000005(a(n)) = 10.

a(n) >= A182679(n).

Extensions

Extended by T. D. Noe, Nov 29 2010