

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
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OFFSET

1,6


LINKS



FORMULA

a(n) = Sum_{dn, 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



KEYWORD

nonn


AUTHOR



STATUS

approved



