OFFSET
1,2
COMMENTS
A balanced number k is a number such that phi(k) | sigma(k).
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..20000
FORMULA
a(n) = Sum_{d|n, phi(d)|sigma(d)} d.
a(n) = Sum_{d|n} d * A351114(d).
a(n) = sigma(n) - Sum_{d|n} d * sign(sigma(d) mod phi(d)).
EXAMPLE
a(4) = 3; the balanced divisors of 4 are 1 and 2 and 1+2 = 3.
a(5) = 1; 1 is the only balanced divisor of 5.
a(6) = 12; the balanced divisors of 6 are 1,2,3,6 and 1+2+3+6 = 12.
MATHEMATICA
a[n_] := DivisorSum[n, # &, Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; Array[a, 100] (* Amiram Eldar, Feb 01 2022 *)
PROG
(PARI) a(n) = sumdiv(n, d, if (!(sigma(d) % eulerphi(d)), d)); \\ Michel Marcus, Feb 01 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 31 2022
STATUS
approved