A342413 - OEIS

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A342413

a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.

1, 1, 1, 2, 1, 1, 1, 4, 6, 1, 1, 4, 1, 3, 8, 8, 1, 3, 1, 8, 2, 1, 1, 4, 10, 3, 9, 4, 1, 1, 1, 16, 2, 1, 12, 12, 1, 3, 8, 4, 1, 1, 1, 4, 3, 1, 1, 16, 14, 5, 4, 8, 1, 9, 8, 4, 2, 1, 1, 4, 1, 3, 3, 32, 6, 1, 1, 8, 2, 1, 1, 12, 1, 3, 5, 4, 6, 1, 1, 16, 54, 1, 1, 4, 2, 3, 8, 20, 1, 3, 4, 4, 2, 1, 24, 16, 1, 7, 15, 20

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..12500

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

FORMULA

a(n) = gcd(A000010(n), A003415(n)).

a(n) = A003415(n) / A342414(n) = A000010(n) / A342415(n).

a(n) = A003557(n) * A342416(n).

MATHEMATICA

Array[GCD[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]], EulerPhi[#]] &@ Abs[#] &, 100] (* Michael De Vlieger, Mar 11 2021 *)