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%I #15 Feb 20 2023 18:31:40
%S 1,3,4,3,1,12,1,3,4,3,1,24,1,17,19,3,1,12,1,3,4,3,1,24,1,3,4,17,1,57,
%T 1,3,4,3,36,24,1,3,4,3,1,68,1,3,19,3,1,24,1,3,4,3,1,12,1,73,4,3,1,69,
%U 1,3,4,3,1,12,1,3,4,122,1,24,1,3,19,3,1,90,1,3,4,3,1,80
%N Sum of the balanced numbers dividing n.
%C A balanced number k is a number such that phi(k) | sigma(k).
%H Antti Karttunen, <a href="/A351113/b351113.txt">Table of n, a(n) for n = 1..20000</a>
%F a(n) = Sum_{d|n, phi(d)|sigma(d)} d.
%F a(n) = Sum_{d|n} d * A351114(d).
%F a(n) = sigma(n) - Sum_{d|n} d * sign(sigma(d) mod phi(d)).
%e a(4) = 3; the balanced divisors of 4 are 1 and 2 and 1+2 = 3.
%e a(5) = 1; 1 is the only balanced divisor of 5.
%e a(6) = 12; the balanced divisors of 6 are 1,2,3,6 and 1+2+3+6 = 12.
%t a[n_] := DivisorSum[n, # &, Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; Array[a, 100] (* _Amiram Eldar_, Feb 01 2022 *)
%o (PARI) a(n) = sumdiv(n, d, if (!(sigma(d) % eulerphi(d)), d)); \\ _Michel Marcus_, Feb 01 2022
%Y Cf. A351112 (number of balanced divisors of n).
%Y Cf. A000005 (tau), A000010 (phi), A000203 (sigma), A020492 (balanced numbers), A023897, A351114.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Jan 31 2022
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