|
|
A228498
|
|
a(n) = sigma(n^2) + phi(n^2) - 2n^2.
|
|
2
|
|
|
0, 1, 1, 7, 1, 31, 1, 31, 13, 57, 1, 163, 1, 91, 73, 127, 1, 307, 1, 321, 111, 183, 1, 691, 31, 241, 121, 535, 1, 1261, 1, 511, 211, 381, 157, 1591, 1, 463, 273, 1377, 1, 2163, 1, 1131, 781, 651, 1, 2803, 57, 1467, 421, 1513, 1, 2791, 273, 2311, 507, 993, 1, 6253, 1, 1123, 1227, 2047, 343, 4711, 1, 2445, 703
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
If n is a prime, p, then a(p) = 1. Proof: a(p) = sigma(p^2) + phi(p^2) - 2p^2 = p^2 + p + 1 + p^2*( 1-(1/p) ) - 2p^2 = p^2 + p + 1 + p^2 - p - 2p^2 = 1.
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=1..n} a(k) ~ ((5*zeta(3) + 2)/ Pi^2 - 2/3) * n^3. - Amiram Eldar, Dec 03 2023
|
|
EXAMPLE
|
a(6) = 31; sigma(6^2) + phi(6^2) - 2*6^2 = 91 + 12 - 72 = 31.
|
|
MAPLE
|
with(numtheory); seq(sigma(k^2) + phi(k^2) - 2*k^2, k=1..20);
|
|
MATHEMATICA
|
Table[DivisorSigma[1, n^2] + EulerPhi[n^2] - 2*n^2, {n, 100}]
|
|
PROG
|
(PARI) vector(100, n, sigma(n^2)+eulerphi(n^2)-2*n^2) \\ Altug Alkan, Oct 28 2015
|
|
CROSSREFS
|
Cf. A051709 (sequence at n instead of n^2).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|