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Search: id:A037019
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| A037019 |
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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). |
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+0
7
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| 1, 2, 4, 6, 16, 12, 64, 30, 36, 48, 1024, 60, 4096, 192, 144, 210, 65536, 180, 262144, 240, 576, 3072, 4194304, 420, 1296, 12288, 900, 960, 268435456, 720, 1073741824, 2310, 9216, 196608, 5184, 1260, 68719476736, 786432, 36864, 1680, 1099511627776
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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
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REFERENCES
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M. E. Grost, The smallest number with a given number of divisors, Amer. Math. Monthly, 75 (1968), 725-729.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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12 = 3*2*2, so a(12) = 2^2*3*5 = 60.
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MATHEMATICA
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(Times@@(Prime[ Range[ Length[ # ] ] ]^Reverse[ #-1 ]))&@Flatten[ FactorInteger[ n ]/.{ a_Integer, b_}:>Table[ a, {b} ] ]
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CROSSREFS
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Cf. A005179, A000040, A072066.
Sequence in context: A136033 A099315 A005179 this_sequence A096174 A096173 A114874
Adjacent sequences: A037016 A037017 A037018 this_sequence A037020 A037021 A037022
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 12 2002
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