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A348492
Greatest common divisor of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).
6
1, 1, 1, 4, 1, 5, 1, 4, 3, 1, 1, 8, 1, 3, 1, 16, 1, 21, 1, 24, 5, 1, 1, 4, 5, 15, 27, 8, 1, 1, 1, 16, 7, 1, 3, 12, 1, 3, 1, 4, 1, 1, 1, 24, 3, 5, 1, 16, 7, 15, 5, 8, 1, 81, 1, 4, 1, 1, 1, 4, 1, 3, 3, 64, 9, 1, 1, 24, 1, 1, 1, 12, 1, 3, 5, 8, 3, 1, 1, 16, 27, 1, 1, 4, 11, 15, 1, 140, 1, 3, 5, 24, 1, 1, 3, 16, 1, 7
OFFSET
1,4
LINKS
FORMULA
a(n) = gcd(A003415(n), A018804(n)).
For n > 1, a(n) = A003415(n) / A348493(n).
a(n) = A003557(n) * A348494(n).
MATHEMATICA
Array[GCD[Total@ GCD[#, Range[#]], # Total[#2/#1 & @@@ FactorInteger[#]]] &, 98] (* 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
A348492(n) = gcd(A003415(n), A018804(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 21 2021
STATUS
approved