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Search: id:A073082
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| A073082 |
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Numbers n such that sum k/d(k) is an integer, where d(k) is the k-th divisor of n (the divisors of n are in increasing order). |
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1
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| 1, 2, 9, 10, 39, 348, 1272, 10682, 18275, 414912, 5606336, 8712340, 20920564, 47201552, 140142814, 240574848
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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No other term less than 500000. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 04 2005
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EXAMPLE
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Divisors of 39 are [1, 3, 13, 39] and 1/1+2/3+3/13+4/39 = 2 is an integer hence 39 is in the sequence.
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MAPLE
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with(numtheory): a:=proc(n) local div: div:=divisors(n): if type(sum(k/div[k], k=1..tau(n)), integer)=true then n else fi end: seq(a(n), n=1..50000); (Deutsch)
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MATHEMATICA
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Do[d = Divisors[n]; If[IntegerQ[Dot[Range[Length[d]], Map[(1/#)&, d]]], Print[n]], {n, 1, 10^8}] (Propper)
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PROGRAM
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(PARI) to have b(n)=sum k/d(k) / b(n)=sum(i=1, numdiv(n), i/component(divisors(n), i))
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CROSSREFS
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Sequence in context: A081346 A058551 A119183 this_sequence A006172 A085069 A072065
Adjacent sequences: A073079 A073080 A073081 this_sequence A073083 A073084 A073085
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2002
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EXTENSIONS
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5 more terms from Ryan Propper (rpropper(AT)stanford.edu), Jul 30 2005
Two further terms from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 31 2005
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