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A023898
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Divisor balance of n is an integer.
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5
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1, 2, 4, 8, 9, 16, 18, 32, 36, 45, 64, 72, 81, 90, 98, 126, 128, 144, 162, 180, 225, 234, 256, 288, 294, 324, 360, 363, 396, 450, 484, 512, 539, 576, 625, 648, 720, 726, 729, 784, 882, 900, 1008, 1024, 1078, 1125, 1152, 1250, 1296, 1440, 1452, 1458, 1800
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OFFSET
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1,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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FORMULA
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Divisor balance of n = sum_{d divides n} {d / phi(d)} where phi is Euler's phi function.
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EXAMPLE
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45 is in this list because its divisors are 1,3,5,9,15 and 45, the corresponding fractions are : (1, 3/2, 5/4, 3/2, 15/8, 15/8) and their sum is 9, which is an integer.
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MATHEMATICA
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Select[ Range[ 2000 ], Function[ n, IntegerQ[ Plus @@ Map[ #/EulerPhi[ # ]&, Divisors[ n ] ] ] ] ]
dbiQ[n_]:=Module[{d=Divisors[n]}, IntegerQ[Total[d/EulerPhi[d]]]]; Select[ Range[ 2000], dbiQ] (* Harvey P. Dale, Jul 25 2016 *)
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CROSSREFS
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Cf. A023899 (corresponding values of the divisor balance).
Cf. A239886, A239887 for a version with proper divisors.
Sequence in context: A114400 A341742 A330710 * A125853 A080025 A152111
Adjacent sequences: A023895 A023896 A023897 * A023899 A023900 A023901
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KEYWORD
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nonn
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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