

A023899


Integer values of Divisor balance.


4



1, 3, 5, 7, 4, 9, 12, 11, 20, 9, 13, 28, 7, 27, 10, 26, 15, 36, 21, 45, 14, 25, 17, 44, 25, 35, 63, 8, 42, 42, 16, 19, 7, 52, 6, 49, 81, 24, 10, 30, 40, 70, 78, 21, 21, 19, 60, 18, 63, 99, 40, 30, 98, 7, 18, 75, 15, 23, 57, 35, 30, 57, 68, 75, 36, 35, 30, 77, 55, 74, 91, 117
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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

a(9)=20 because the 9th integer having an integer Divisor balance is 36 : its divisors are 1,2,3,4,6,9,12,18 and 36, giving the fractions (1, 2, 3/2, 2, 3, 3/2, 3, 3, 3) which sum to 20.


MATHEMATICA

Select[ Array[ Function[ n, Plus @@ Map[ #/EulerPhi[ # ]&, Divisors[ n ] ] ], 3000 ], IntegerQ ]


CROSSREFS

cf. A023898 (integers for which the divisor balance is an integer).
cf. A239886, A239887 for a version with proper divisors.
Sequence in context: A101088 A134487 A064537 * A324712 A279321 A254863
Adjacent sequences: A023896 A023897 A023898 * A023900 A023901 A023902


KEYWORD

nonn


AUTHOR

Olivier Gérard


STATUS

approved



