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 A367483 Sum of the arithmetic derivatives of the nontrivial divisors of n whose arithmetic derivative is coprime to n. 2
 0, 1, 1, 1, 1, 7, 1, 1, 1, 9, 1, 7, 1, 11, 10, 1, 1, 7, 1, 9, 12, 15, 1, 7, 1, 17, 1, 11, 1, 41, 1, 1, 16, 21, 14, 7, 1, 23, 18, 9, 1, 49, 1, 15, 10, 27, 1, 7, 1, 9, 22, 17, 1, 7, 18, 11, 24, 33, 1, 41, 1, 35, 12, 1, 20, 82, 1, 21, 28, 71, 1, 7, 1, 41, 10, 23, 20, 79 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 LINKS Table of n, a(n) for n=1..78. FORMULA a(n) = Sum_{d|n, d>1, gcd(n,d')=1} d'. EXAMPLE a(66) = 82. The nontrivial divisors of 66 are {2, 3, 6, 11, 22, 33, 66} with derivatives {1, 1, 5, 1, 13, 14, 61}, 6 of which are coprime to n. The sum of the coprime derivatives gives 1 + 1 + 5 + 1 + 13 + 61 = 82. MATHEMATICA ad[1] = 0; ad[n_] := ad[n] = n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, ad[#] &, CoprimeQ[n, ad[#]] &]; Array[a, 100] (* Amiram Eldar, Nov 25 2023 *) CROSSREFS Cf. A003415 (n'), A367482. Sequence in context: A336457 A271498 A365332 * A348281 A317940 A318674 Adjacent sequences: A367480 A367481 A367482 * A367484 A367485 A367486 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Nov 24 2023 STATUS approved

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Last modified May 23 15:34 EDT 2024. Contains 372763 sequences. (Running on oeis4.)