A367633 Sum of the nontrivial divisors of n whose arithmetic derivative is coprime to n.

0, 2, 3, 2, 5, 11, 7, 2, 3, 17, 11, 11, 13, 23, 23, 2, 17, 11, 19, 17, 31, 35, 23, 11, 5, 41, 3, 23, 29, 50, 31, 2, 47, 53, 47, 11, 37, 59, 55, 17, 41, 60, 43, 35, 23, 71, 47, 11, 7, 17, 71, 41, 53, 11, 71, 23, 79, 89, 59, 50, 61, 95, 31, 2, 83, 110, 67, 53, 95, 98, 71, 11, 73, 113, 23, 59

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Formula

a(n) = Sum_{d|n, d>1, gcd(n,d')=1} d.

Example

a(22) = 35. The nontrivial divisors of 22 are {2, 11, 22} whose derivatives are {1, 1, 13} and all of which are coprime to 22. The sum of the nontrivial divisors is 2 + 11 + 22 = 35.

Mathematica

ad[1] = 0; ad[n_] := ad[n] = n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := DivisorSum[n, # &, CoprimeQ[n, ad[#]] &]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Nov 25 2023 *)

Crossrefs

Cf. A003415 (n'), A367483.

Sequence in context: A059098 A082050 A353956 * A183098 A183101 A343300

Adjacent sequences: A367630 A367631 A367632 * A367634 A367635 A367636

Keyword

nonn

Author

Wesley Ivan Hurt, Nov 25 2023

Status

approved