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Search: id:A129902
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| A129902 |
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Smallest multiple of n having exactly twice as many divisors as n. |
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+0
2
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| 2, 6, 6, 12, 10, 24, 14, 24, 18, 30, 22, 60, 26, 42, 30, 48, 34, 72, 38, 60, 42, 66, 46, 120, 50, 78, 54, 84, 58, 120, 62, 96, 66, 102, 70, 180, 74, 114, 78, 120, 82, 168, 86, 132, 90, 138, 94, 240, 98, 150, 102, 156, 106, 216, 110, 168, 114, 174, 118, 360, 122, 186, 126
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n)={min(m*n): A000005(m*n)=2*A000005(n)}. - R. J. Mathar
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EXAMPLE
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n=6 has 4 divisors. a(6) is not 12 or 18 because 12 and 18 have only 6 divisors as opposed to the 8 divisors required by the definition.
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MAPLE
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A129902 := proc(n) local m; m := 2 ; while numtheory[tau](m*n)<> 2*numtheory[tau](n) do m := m+1 ; od ; RETURN(m*n) ; end: for n from 1 to 100 do printf("%d, ", A129902(n)) ; od ; - R. J. Mathar
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MATHEMATICA
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a[n_] := Module[{}, in = 2; While[Length[Divisors[in*n]] != 2*Length[Divisors[n]], in++ ]; in*n]; Table[a[i], {i, 1, 70}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 07 2007
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CROSSREFS
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Cf. A000005.
Sequence in context: A134466 A062562 A106832 this_sequence A087560 A071892 A064797
Adjacent sequences: A129899 A129900 A129901 this_sequence A129903 A129904 A129905
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KEYWORD
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nonn
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AUTHOR
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J. Lowell, jhbubby(AT)mindspring.com, Jun 04 2007
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Jon E. Schoenfield (jonscho(AT)hiwaay.net), Jun 07 2007
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