%I
%S 1,2,4,6,10,12,14,18,22,26,30,38,42,50,54,58,60,62,66,78,90,102,114,
%T 126,130,138,150,170,174,186,210,246,258,282,294,318,330,354,366,390,
%U 426,438,462,498,510,534,546,570,606,618,642,654,678,690,714,750,762,786
%N Record holders for n^2  phi(n)*sigma(n)
%C These numbers exhibit the largest differences between n^2 and sigma(n)*phi(n).
%C All of the differences are in A069249, and are guaranteed to be positive by Th. 329 in Hardy & Wright. The record differences are in A164876.
%H Amiram Eldar, <a href="/A164875/b164875.txt">Table of n, a(n) for n = 1..10000</a>
%e sigma(10) = 18; phi(10) = 4; 10^2  sigma(10)*phi(10) = 28. This difference, 28, exceeds the difference for every smaller n, so 10 is in this sequence and 28 is in A164876.
%t f[n_] := n^2  EulerPhi[n] * DivisorSigma[1, n]; s = {}; fm = 1; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, n]], {n, 1, 786}]; s (* _Amiram Eldar_, Aug 29 2019 *)
%Y Cf. A069249, A164876, A000203, A000010.
%K nonn
%O 1,2
%A _Walter Nissen_, Aug 29 2009
