A164876 Record differences for n^2 - phi(n)*sigma(n)

0, 1, 2, 12, 28, 32, 52, 90, 124, 172, 324, 364, 612, 640, 756, 844, 912, 964, 1476, 2052, 2484, 3492, 4356, 4644, 4804, 6372, 7620, 8164, 10116, 11556, 16452, 20196, 22212, 26532, 28980, 33732, 39780, 41796, 44676, 55332, 60516, 63972, 75204, 82692

Offset

1,3

Comments

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

All of the differences are in A069249.

Links

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

Formula

a(n) = A069249(A164875(n)). - Amiram Eldar, Aug 29 2019

Example

sigma(10) = 18; phi(10) = 4; 10^2 - sigma(10)*phi(10) = 28. This difference, 28, exceeds the difference for every smaller n, so 28 is in this sequence and 10 is in A164875.

Mathematica

f[n_] := n^2 - EulerPhi[n] * DivisorSigma[1, n]; s = {}; fm = -1; Do[f1 = f[n]; If[f1 > fm, fm = f1; AppendTo[s, fm]], {n, 1, 500}]; s (* Amiram Eldar, Aug 29 2019 *)

Crossrefs

Cf. A069249, A164875, A000203, A000010.

Sequence in context: A154149 A354780 A119201 * A225291 A211623 A034318

Adjacent sequences: A164873 A164874 A164875 * A164877 A164878 A164879

Keyword

nonn

Author

Walter Nissen, Aug 29 2009

Extensions

a(1) = 0 added by Amiram Eldar, Aug 29 2019

Status

approved