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A023898 Divisor balance of n is an integer. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

Divisor balance of n = sum_{d divides n} {d / phi(d)} where phi is Euler's phi function.

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A023899 (corresponding values of the divisor balance).

Cf. A239886, A239887 for a version with proper divisors.

Sequence in context: A175338 A071601 A114400 * A125853 A080025 A152111

Adjacent sequences:  A023895 A023896 A023897 * A023899 A023900 A023901

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified April 20 04:42 EDT 2019. Contains 322294 sequences. (Running on oeis4.)