This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386401 #15 Jul 21 2025 08:57:02
%S A386401 1,3,8,7,24,2,48,15,26,18,120,7,168,36,64,31,288,13,360,21,128,90,528,
%T A386401 5,124,126,80,6,840,16,960,63,320,216,1152,91,1368,270,448,9,1680,32,
%U A386401 1848,105,208,396,2208,31,342,93,256,147,2808,20,576,45,320,630,3480,56
%N A386401 a(n) = numerator(sigma(n)*phi(n)/n^2).
%C A386401 a(n)/A386402(n) = sigma(n)*phi(n)*(1/n^2) is a multiplicative function since it is the product of three multiplicative functions.
%D A386401 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 5.3.21 on page 169.
%H A386401 Amiram Eldar, <a href="/A386401/b386401.txt">Table of n, a(n) for n = 1..10000</a>
%F A386401 From _Amiram Eldar_, Jul 21 2025: (Start)
%F A386401 Let f(n) = a(n)/A386402(n) = sigma(n)*phi(n)/n^2. Then:
%F A386401 f(n) = A062354(n)/n^2.
%F A386401 f(n) is multiplicative with f(p^e) = 1 - 1/p^(e+1).
%F A386401 Dirichlet g.f. of f(n): zeta(s) * zeta(s+1) * Product_{p prime} (1 - 1/p^(s+1) - 1/p^(s+2)+ 1/p^(2*s+2)).
%F A386401 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} f(k) = Product_{p prime} (1 - 1/(p^2*(p+1))) = 0.881513... (A065465). (End)
%t A386401 a[n_]:=Numerator[DivisorSigma[1,n]EulerPhi[n]/n^2]; Array[a,60]
%o A386401 (PARI) a(n) = {my(f = factor(n)); numerator(sigma(f) * eulerphi(f) / n^2);} \\ _Amiram Eldar_, Jul 21 2025
%Y A386401 Cf. A000010, A000203, A000290, A062354, A065465.
%Y A386401 Cf. A386402 (denominators).
%K A386401 nonn,easy,frac
%O A386401 1,2
%A A386401 _Stefano Spezia_, Jul 20 2025