A182673 a(n) = the smallest n-digit number with exactly 7 divisors, a(n) = 0 if no such number exists.

0, 64, 729, 0, 15625, 117649, 1771561, 24137569, 148035889, 2565726409, 10779215329, 128100283921, 1061520150601, 10942526586601, 122978496247489, 1014741853230169, 10372926089038969, 101513598260088169, 1055229678769825441, 10131553366728232321, 101842394378135916961

Offset

1,2

Comments

a(n) = the smallest n-digit number of the form p^6 (p = prime), a(n) = 0 if no such number exists.

Links

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

Formula

A000005(a(n)) = 7.

Maple

A182673 := proc(n) for i from 1 do p := ithprime(i)^6 ; if A055642(p) > n then return 0 ; elif A055642(p) = n then return p; end if; end do: end proc:

Mathematica

Transpose[If[#[[1]]==#[[2]], {0, #[[2]]}, #]&/@Partition[ Table[ NextPrime[ Surd[10^n, 6]]^6, {n, 0, 40}], 2, 1]][[1]](* Harvey P. Dale, Oct 05 2015 *)

Crossrefs

Cf. A030516, A182674.

Sequence in context: A317229 A008513 A321830 * A182674 A351194 A048392

Adjacent sequences: A182670 A182671 A182672 * A182674 A182675 A182676

Keyword

nonn,base

Author

Jaroslav Krizek, Nov 27 2010

Status

approved