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 A089707 Smallest number beginning with 1 and having exactly n divisors. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n a prime, a(n) must be of the form p^(n-1) for some prime, p. LINKS 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 A084969 A045592 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

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)