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A348495
a(n) = gcd(A018804(n), A347130(n)), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n (A003415), and A018804 is Pillai's arithmetical function.
5
1, 1, 1, 2, 1, 5, 1, 4, 3, 1, 1, 8, 1, 3, 1, 16, 1, 63, 1, 72, 5, 1, 1, 4, 5, 15, 27, 8, 1, 1, 1, 16, 7, 1, 3, 6, 1, 3, 1, 4, 1, 1, 1, 24, 9, 5, 1, 80, 7, 15, 5, 8, 1, 81, 1, 4, 1, 1, 1, 24, 1, 3, 3, 32, 9, 1, 1, 24, 1, 1, 1, 12, 1, 3, 5, 8, 3, 1, 1, 16, 27, 1, 1, 8, 11, 15, 1, 140, 1, 9, 5, 72, 1, 1, 3, 16, 1
OFFSET
1,4
LINKS
FORMULA
a(n) = gcd(A018804(n), A347130(n)).
a(n) = A003557(n) * A348496(n).
MATHEMATICA
Table[GCD[Total@ GCD[n, Range[n]], DivisorSum[n, #*(If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[n/#]) &]], {n, 97}] (* Michael De Vlieger, Oct 21 2021 *)
PROG
(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A347130(n) = sumdiv(n, d, d*A003415(n/d));
A348495(n) = gcd(A018804(n), A347130(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 21 2021
STATUS
approved