A164875 Record holders for n^2 - phi(n)*sigma(n).

1, 2, 4, 6, 10, 12, 14, 18, 22, 26, 30, 38, 42, 50, 54, 58, 60, 62, 66, 78, 90, 102, 114, 126, 130, 138, 150, 170, 174, 186, 210, 246, 258, 282, 294, 318, 330, 354, 366, 390, 426, 438, 462, 498, 510, 534, 546, 570, 606, 618, 642, 654, 678, 690, 714, 750, 762, 786

Offset: 1

Author

Walter Nissen, Aug 29 2009

Keywords

• nonn

Comments

These numbers exhibit the largest differences between n^2 and sigma(n)*phi(n).

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069249, A164876, A000203, A000010.

Programs

Mathematica

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 *)