A182683 a(n) = the smallest n-digit number with exactly 12 divisors, a(n) = 0 if no such number exists.

0, 60, 108, 1012, 10004, 100004, 1000012, 10000025, 100000012, 1000000025, 10000000012, 100000000004, 1000000000017, 10000000000004, 100000000000012, 1000000000000004, 10000000000000025, 100000000000000004, 1000000000000000017, 10000000000000000034, 100000000000000000012, 1000000000000000000025, 10000000000000000000004, 100000000000000000000004

Offset

1,2

Comments

a(n) = the smallest 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..24.

Formula

A000005(a(n)) = 12.

a(n) <= A182684(n).

Mathematica

Table[k=10^(n-1); While[k<10^n && DivisorSigma[0, k] != 12, k++]; If[k==10^n, k=0]; k, {n, 20}]

Crossrefs

Cf. A030630, A182684.

Sequence in context: A008887 A217738 A351548 * A174601 A306908 A252961

Adjacent sequences: A182680 A182681 A182682 * A182684 A182685 A182686

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Status

approved