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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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0
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1, 2, 9, 10, 39, 348, 1272, 10682, 18275, 414912, 5606336, 8712340, 20920564, 47201552, 140142814, 240574848
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| No other term less than 500000. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 04 2005
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EXAMPLE
| 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
| 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
| Do[d = Divisors[n]; If[IntegerQ[Dot[Range[Length[d]], Map[(1/#)&, d]]], Print[n]], {n, 1, 10^8}] (Propper)
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PROG
| (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
| Sequence in context: A058551 A119183 A179888 * A191401 A006172 A085069
Adjacent sequences: A073079 A073080 A073081 * A073083 A073084 A073085
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2002
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EXTENSIONS
| 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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