A089707 Smallest number beginning with 1 and having exactly n divisors.

1, 11, 121, 10, 16, 12, 15625, 102, 100, 112, 1024, 108, 13841287201, 192, 144, 120, 152587890625, 180, 1628413597910449, 1040, 1600, 11264, 1174562876521148458974062689, 1020, 1296, 12288, 1764, 1344, 144209936106499234037676064081, 1008, 1073741824, 1080, 123904, 196608, 11664

Offset

1,2

Comments

For n a prime, a(n) must be of the form p^(n-1) for some prime, p.

Links

Table of n, a(n) for n=1..35.

Maple

with(numtheory): a:= proc(k) local s, m, n, d, i: if isprime(k) then for i from 1 do m:=ithprime(i)^(k-1): s:=convert(m, base, 10): if(s[nops(s)]=1) then RETURN(m) fi od else for d from 0 to 20 do for n from 0 to 10^d-1 do m:=10^d+n: if tau(m)=k then RETURN(m) fi od od: RETURN(0) fi: end: seq(a(k), k=1..33); # C. Ronaldo
with(numtheory): a:= proc(k) options remember: local s, m, n, d, i: if isprime(k) then for i from 1 do m:=ithprime(i)^(k-1): s:=convert(m, base, 10): if(s[nops(s)]=1) then RETURN(m) fi od else for d from 0 do for n from 0 to 10^d-1 do m:=10^d+n: if tau(m)=k then RETURN(m) fi od od: RETURN(0) fi: end: seq(a(k), k=1..35); # C. Ronaldo

Mathematica

a = Table[0, {25}], Do[ If[ IntegerDigits[n][[1]] == 1, b = DivisorSigma[0, n]; If[ a[[b]] == 0, a[[b]] = n; Print[b, " = ", n]]], {n, 1, 2*10^7}] (* Robert G. Wilson v, Nov 15 2003 *)

Crossrefs

Cf. A000005, A005179.

Sequence in context: A171316 A081122 A004190 * A223391 A337707 A084969

Adjacent sequences: A089704 A089705 A089706 * A089708 A089709 A089710

Keyword

base,nonn

Author

Amarnath Murthy, Nov 14 2003

Extensions

Edited, corrected and extended by Robert G. Wilson v and Ray Chandler, Nov 15 2003

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005

Status

approved