|
|
A189393
|
|
a(n) = phi(n^4).
|
|
6
|
|
|
1, 8, 54, 128, 500, 432, 2058, 2048, 4374, 4000, 13310, 6912, 26364, 16464, 27000, 32768, 78608, 34992, 123462, 64000, 111132, 106480, 267674, 110592, 312500, 210912, 354294, 263424, 682892, 216000, 893730, 524288, 718740, 628864, 1029000, 559872
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n^3*phi(n).
Dirichlet g.f.: zeta(s - 4) / zeta(s - 3). The n-th term of the Dirichlet inverse is n^3 * A023900(n) = (-1)^omega(n) * a(n) / A003557(n), where omega=A001221. - Álvar Ibeas, Nov 24 2017
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^5 - p^4 - p + 1)) = 1.15762316629211803144... - Amiram Eldar, Dec 06 2020
|
|
MATHEMATICA
|
EulerPhi[Range[100]^4] (* T. D. Noe, Dec 27 2011 *)
|
|
PROG
|
(Magma) [ n^3*EulerPhi(n) : n in [1..100] ]
(PARI) vector(66, n, n^3*eulerphi(n)) /* Joerg Arndt, Apr 22 2011 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|