Search: id:A037019
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%I A037019
%S A037019 1,2,4,6,16,12,64,30,36,48,1024,60,4096,192,144,210,65536,180,262144,
%T A037019 240,576,3072,4194304,420,1296,12288,900,960,268435456,720,1073741824,
%U A037019 2310,9216,196608,5184,1260,68719476736,786432,36864,1680,1099511627776
%N A037019 Let n = p_1*p_2*...*p_k be the prime factorization of n, with the primes 
               sorted in descending order. Then a(n) = 2^(p_1 - 1)*3^(p_2 - 1)*...*A000040(k)^(p_k 
               - 1).
%C A037019 This is an easy way to produce a number with exactly n divisors and it 
               usually produces the smallest such number (A005179(n).) The reference 
               calls n "ordinary" if A005179(n) = a(n) and "exceptional" otherwise. 
               - David Wasserman (wasserma(AT)spawar.navy.mil), Jun 12 2002
%D A037019 M. E. Grost, The smallest number with a given number of divisors, Amer. 
               Math. Monthly, 75 (1968), 725-729.
%H A037019 T. D. Noe, <a href="b037019.txt">Table of n, a(n) for n=1..1000</a>
%e A037019 12 = 3*2*2, so a(12) = 2^2*3*5 = 60.
%t A037019 (Times@@(Prime[ Range[ Length[ # ] ] ]^Reverse[ #-1 ]))&@Flatten[ FactorInteger[ 
               n ]/.{ a_Integer, b_}:>Table[ a, {b} ] ]
%Y A037019 Cf. A005179, A000040, A072066.
%Y A037019 Sequence in context: A136033 A099315 A005179 this_sequence A096174 A096173 
               A114874
%Y A037019 Adjacent sequences: A037016 A037017 A037018 this_sequence A037020 A037021 
               A037022
%K A037019 nonn,nice,easy
%O A037019 1,2
%A A037019 Wouter Meeussen (wouter.meeussen(AT)pandora.be)
%E A037019 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 12 
               2002

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