OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 25 2023
STATUS
approved