A182679 a(n) = the smallest n-digit number with exactly 10 divisors, a(n) = 0 if no such number exists.

0, 48, 112, 1053, 10096, 100112, 1000016, 10000017, 100000144, 1000000016, 10000000071, 100000000336, 1000000000304, 10000000000624, 100000000000528, 1000000000000016, 10000000000000503

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• base

Comments

a(n) = the smallest n-digit number of the form p^9 or p^4*q^1 (p, q = distinct primes), a(n) = 0 if no such number exists.

Crossrefs

See A182680(n) - the largest n-digit number with exactly 10 divisors.

Programs

Mathematica

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

Sage

A182679 = lambda n: next((x for x in IntegerRange(10**(n-1), 10**n) if number_of_divisors(x) == 10),0)
# D. S. McNeil, Nov 28 2010

Formula

A000005(a(n)) = 10.