A182678 a(n) = the largest n-digit number with exactly 9 divisors, a(n) = 0 if no such number exists.

0, 36, 676, 9025, 98596, 996004, 9991921, 99960004, 999887641, 9999600004, 99998883076, 999994000009, 9999970526529, 99999960000004, 999999645718441, 9999999400000009, 99999998091984169, 999999982000000081, 9999999904066746025, 99999999940000000009, 999999999956753113201, 9999999999400000000009, 99999999997572677916169, 999999999994000000000009, 9999999999940679895905281

Offset

1,2

Comments

a(n) = the largest n-digit number of the form p^8 or p^2*q^2 (p, q = distinct primes), a(n) = 0 if no such number exists.

Links

Table of n, a(n) for n=1..25.

Formula

A000005(a(n)) = 9.

Mathematica

Table[k=10^n-1; While[k>10^(n-1) && DivisorSigma[0, k] != 9, k--]; If[k==10^(n-1), k=0]; k, {n, 10}]

Crossrefs

Cf. A182677 (smallest n-digit number with exactly 9 divisors).

Sequence in context: A010988 A000815 A271794 * A239181 A053947 A157092

Adjacent sequences: A182675 A182676 A182677 * A182679 A182680 A182681

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Extensions

Extended by T. D. Noe, Nov 29 2010

a(11)-a(25) from Robert Gerbicz, Nov 29 2010

Status

approved