A182684 - OEIS

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A182684

a(n) = the largest n-digit number with exactly 12 divisors, a(n) = 0 if no such number exists.

0, 96, 996, 9999, 99999, 999998, 9999999, 99999988, 999999996, 9999999991, 99999999999, 999999999981, 9999999999997, 99999999999968, 999999999999981, 9999999999999989, 99999999999999999, 999999999999999988, 9999999999999999981, 99999999999999999977, 999999999999999999963

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

a(n) = the largest n-digit number of the form p^11, p^5*q, p^3*q^2 or p^2*q*r (p, q, r distinct primes), a(n) = 0 if no such number exists.

LINKS

Table of n, a(n) for n=1..21.

FORMULA

A000005(a(n)) = 12.

a(n) >= A182683(n).

MATHEMATICA

Join[{0}, Table[Module[{n=10^i, k=1}, While[DivisorSigma[0, n-k]!=12, k++]; n-k], {i, 2, 30}]] (* Harvey P. Dale, Jun 02 2014 *)