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A089707 Smallest number beginning with 1 and having exactly n divisors. 0

%I

%S 1,11,121,10,16,12,15625,102,100,112,1024,108,13841287201,192,144,120,

%T 152587890625,180,1628413597910449,1040,1600,11264,

%U 1174562876521148458974062689,1020,1296,12288,1764,1344,144209936106499234037676064081,1008,1073741824,1080,123904,196608,11664

%N Smallest number beginning with 1 and having exactly n divisors.

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

%p 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

%p 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

%t 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 *)

%Y Cf. A000005, A005179.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 14 2003

%E Edited, corrected and extended by _Robert G. Wilson v_ and _Ray Chandler_, Nov 15 2003

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

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Last modified May 22 19:19 EDT 2019. Contains 323481 sequences. (Running on oeis4.)