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A268177
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Numbers m such that Sum_{i=1..q} 1/lambda(d(i)) is an integer, where d(i) are the q divisors of m and lambda is the Carmichael lambda function (A002322).
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2
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1, 2, 6, 8, 12, 15, 24, 28, 30, 40, 70, 84, 112, 120, 140, 210, 240, 252, 280, 315, 336, 351, 357, 360, 420, 550, 630, 684, 702, 714, 836, 840, 884, 912, 952, 988, 1092, 1100, 1120, 1140, 1364, 1386, 1650, 1710, 1820, 2002, 2040, 2088, 2090, 2200, 2394, 2484
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OFFSET
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1,2
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COMMENTS
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The corresponding integers are 1, 2, 3, 3, 4, 2, 5, 3, 4, 4, 3, 5, 4, 7, 4, 5, 8, 6, 5, 3, 7, 2, 2, 8, 7,...
A majority of numbers of the sequence are even, except 1, 15, 315, 351, 357, 2871, 3663,...
Replacing the function lambda(n) by the Euler totient function phi(n) (A000010) gives only the short sequence {1, 2, 6} for n < 10^7.
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LINKS
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EXAMPLE
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6 is in the sequence because the divisors of 6 are {1,2,3,6} => 1/lambda(1)+1/lambda(2)+1/lambda(3)+ 1/lambda(6) = 1/1 + 1/1 + 1/2 + 1/2 = 3 is an integer.
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MATHEMATICA
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lst={}; Do[If[IntegerQ[Total[1/CarmichaelLambda[Divisors[n]]]], AppendTo[lst, n]], {n, 0, 2500}]; lst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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