A182681 a(n) is the smallest n-digit number with exactly 11 divisors, a(n) = 0 if no such number exists.

0, 0, 0, 1024, 59049, 0, 9765625, 0, 282475249, 0, 25937424601, 137858491849, 2015993900449, 41426511213649, 420707233300201, 4808584372417849, 13422659310152401, 174887470365513049, 1822837804551761449, 15516041187205853449, 110462212541120451001, 1091533853073393531649

Offset

1,4

Comments

a(n) is the smallest n-digit number of the form p^10 (p = prime), a(n) = 0 if no such number exists.

Links

Table of n, a(n) for n=1..22.

Formula

A000005(a(n)) = 11.

a(n) = min { 0 } union ( A030629 intersect [10^(n-1), 10^n-1] )

Prog

(PARI) a(n)=(10^n>n=nextprime(sqrtn(10^(n-1), 10))^10)*n  \\ M. F. Hasler, Nov 27 2010

Crossrefs

See A182682(n) - the largest n-digit number with exactly 11 divisors.

Cf. A030629 (numbers with 11 divisors).

Sequence in context: A195658 A264205 A321834 * A182682 A305941 A351198

Adjacent sequences: A182678 A182679 A182680 * A182682 A182683 A182684

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Status

approved