A367483 Sum of the arithmetic derivatives of the nontrivial divisors of n whose arithmetic derivative is coprime to n.

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

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