A386402 - OEIS

%I #10 Jul 21 2025 08:56:57

%S 1,4,9,8,25,3,49,16,27,25,121,9,169,49,75,32,289,18,361,25,147,121,

%T 529,6,125,169,81,7,841,25,961,64,363,289,1225,108,1369,361,507,10,

%U 1681,49,1849,121,225,529,2209,36,343,125,289,169,2809,27,605,49,361,841,3481,75

%N a(n) = denominator(sigma(n)*phi(n)/n^2).

%C A386401(n)/a(n) = sigma(n)*phi(n)/n^2 is a multiplicative function since it is the product of three multiplicative functions.

%D James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 5.3.21 on page 169.

%H Amiram Eldar, <a href="/A386402/b386402.txt">Table of n, a(n) for n = 1..10000</a>

%t a[n_]:=Denominator[DivisorSigma[1,n]EulerPhi[n]/n^2]; Array[a,60]

%o (PARI) a(n) = {my(f = factor(n)); denominator(sigma(f) * eulerphi(f) / n^2);} \\ _Amiram Eldar_, Jul 21 2025

%Y Cf. A000010, A000203, A000290.

%Y Cf. A386401 (numerators).

%K nonn,easy,frac

%O 1,2

%A _Stefano Spezia_, Jul 20 2025