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A362707
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a(n) = Sum_{d|n, phi(d)|sigma(d)} (n-d).
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0
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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, 49, 50, 67, 28, 123, 30, 61, 62, 65, 34, 156, 36, 73, 74, 77, 40, 184, 42, 85, 116, 89, 46, 216, 48, 97, 98, 101, 52, 204, 54, 151, 110, 113, 58, 351, 60, 121, 122, 125, 64, 252, 66, 133
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OFFSET
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1,3
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COMMENTS
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Total distance from n to each balanced divisor of n (see example).
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LINKS
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FORMULA
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a(n) = Sum_{d|n} (n-d) * A351114(d).
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EXAMPLE
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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.
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MATHEMATICA
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a[n_] := DivisorSum[n, (n - #) &, Divisible[DivisorSigma[1, #], EulerPhi[#]] &]; Array[a, 100]
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PROG
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(PARI) a(n) = sumdiv(n, d, if (!(sigma(d) % eulerphi(d)), n-d)); \\ Michel Marcus, Apr 30 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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