A077101 a(n) = A051612(n)*A065387(n) = sigma(n)^2-phi(n)^2, where A051612(n) = sigma(n) - phi(n) and A065387(n) = sigma(n) + phi(n).

0, 8, 12, 45, 20, 140, 28, 209, 133, 308, 44, 768, 52, 540, 512, 897, 68, 1485, 76, 1700, 880, 1196, 92, 3536, 561, 1620, 1276, 2992, 116, 5120, 124, 3713, 1904, 2660, 1728, 8137, 148, 3276, 2560, 7844, 164, 9072, 172, 6656, 5508, 4700, 188, 15120, 1485

Offset: 1

Author

Labos Elemer, Nov 06 2002

Keywords

• nonn
• easy

Comments

If n is prime, then a(n) = 4n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A000203, A002117, A051612, A062354, A065387, A065464, A072861, A077099, A077100, A127473.

Programs

Mathematica

Table[DivisorSigma[1,n]^2-EulerPhi[n]^2,{n,50}] (* Harvey P. Dale, Nov 08 2013 *)

PARI

A077101(n) = (sigma(n)^2 - eulerphi(n)^2); \\ Antti Karttunen, May 26 2017

Formula

a(n) = A077099(n) * A077100(n). - Antti Karttunen, May 26 2017

From Amiram Eldar, Dec 04 2023: (Start)

a(n) = A072861(n) - A127473(n).

Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = 5*zeta(3)/2 - Product_{p prime}(1 - (2*p-1)/p^3) = (5/2)*A002117 - A065464 = 2.576892... . (End)

Extensions

Edited by Dean Hickerson, Nov 07 2002