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%I #6 May 02 2023 23:54:22
%S 0,1,2,5,4,12,6,13,14,17,10,36,12,25,26,29,16,60,18,37,38,41,22,96,24,
%T 49,50,67,28,123,30,61,62,65,34,156,36,73,74,77,40,184,42,85,116,89,
%U 46,216,48,97,98,101,52,204,54,151,110,113,58,351,60,121,122,125,64,252,66,133
%N a(n) = Sum_{d|n, phi(d)|sigma(d)} (n-d).
%C Total distance from n to each balanced divisor of n (see example).
%F a(n) = Sum_{d|n} (n-d) * A351114(d).
%F a(n) = n*A351112(n) - A351113(n).
%e a(12) = 36; 12 has 5 balanced divisors 1,2,3,6,12 and the sum of their distances to n is (12-1)+(12-2)+(12-3)+(12-6)+(12-12) = 36.
%t a[n_] := DivisorSum[n, (n - #) &, Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; Array[a, 100]
%o (PARI) a(n) = sumdiv(n, d, if (!(sigma(d) % eulerphi(d)), n-d)); \\ _Michel Marcus_, Apr 30 2023
%Y Cf. A000005 (tau), A000010 (phi), A020492 (balanced numbers), A351112, A351113, A351114.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Apr 30 2023