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A367633
Sum of the nontrivial divisors of n whose arithmetic derivative is coprime to n.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 25 2023
STATUS
approved