OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..339
Romeo Meštrović, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057 [math.NT], 2011.
FORMULA
a(n) = A309148(n,n).
a(n) = (1/n) * A318477(n).
a(p) == 1 (mod p^3) for all primes p >= 5 (apply Meštrović, Remark 17, p. 12). - Peter Bala, Mar 28 2023
a(n) ~ exp(n - 1/2) * n^(n - 5/2) / sqrt(2*Pi). - Vaclav Kotesovec, Mar 28 2023
MAPLE
with(numtheory):
a:= proc(n) option remember; add(phi(n/d)*
(-1)^(n+d)*binomial(n*d, d), d=divisors(n))/n^2
end:
seq(a(n), n=1..20);
MATHEMATICA
a[n_] := a[n] = Sum[EulerPhi[n/d]*
(-1)^(n + d)*Binomial[n*d, d], {d, Divisors[n]}]/n^2;
Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Mar 24 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 14 2019
STATUS
approved