OFFSET
1,2
COMMENTS
Order of the group SL(4,Z_n). For n > 2, a(n) is divisible by 11520. - Jianing Song, Nov 24 2018
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = (n^16/phi(n))*Product_{primes p dividing n} ((1 - 1/p^4)*(1 - 1/p^3)*(1 - 1/p^2)*(1 - 1/p)). Multiplicative with a(p^e) = p^(15*e-9)*(p^4 - 1)*(p^3 - 1)*(p^2 - 1). - Vladeta Jovovic, Nov 18 2001
a(n) = n^15*Product_{primes p dividing n} ((1 - 1/p^4)*(1 - 1/p^3)*(1 - 1/p^2)) = A305186(n)/phi(n). - Jianing Song, Nov 24 2018
Sum_{k=1..n} a(k) ~ c * n^16, where c = (1/16) * Product_{p prime} ((p^10 - p^7 - p^6 - p^5 + p^4 + p^3 + p^2 - 1)/p^10) = 0.04715136234... . - Amiram Eldar, Oct 23 2022
MATHEMATICA
f[p_, e_] := (1 - 1/p^4)*(1 - 1/p^3)*(1 - 1/p^2); a[1] = 1; a[n_] := n^15 * Times @@ f @@@ FactorInteger[n]; Array[a, 17] (* Amiram Eldar, Oct 23 2022 *)
PROG
(PARI) a(n) = f = factor(n); n^16/eulerphi(n) * prod(i=1, #f~, (1-1/f[i, 1]^4)*(1-1/f[i, 1]^3)*(1-1/f[i, 1]^2)*(1-1/f[i, 1])); \\ Michel Marcus, Sep 02 2013
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
benlove(AT)preston.polaristel.net (Benjamin T. Love)
EXTENSIONS
More terms from Vladeta Jovovic, Nov 18 2001
STATUS
approved