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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).
2
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
1,2
COMMENTS
If n is prime, then a(n) = 4n.
LINKS
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)
MATHEMATICA
Table[DivisorSigma[1, n]^2-EulerPhi[n]^2, {n, 50}] (* Harvey P. Dale, Nov 08 2013 *)
PROG
(PARI) A077101(n) = (sigma(n)^2 - eulerphi(n)^2); \\ Antti Karttunen, May 26 2017
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Nov 06 2002
EXTENSIONS
Edited by Dean Hickerson, Nov 07 2002
STATUS
approved