OFFSET
1,1
COMMENTS
A sequence of length n is aperiodic if all n rotations of its entries are distinct.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
FORMULA
A(n,k) = Sum_{d|n, e|k} mu(d) * mu(e) * 2^((n/d) * (k/e)).
EXAMPLE
Array begins:
2 2 6 12 30
2 10 54 228 990
6 54 498 4020 32730
12 228 4020 65040 1047540
30 990 32730 1047540 33554370
MATHEMATICA
nn=5;
a[n_, k_]:=Sum[MoebiusMu[d]*MoebiusMu[e]*2^(n/d*k/e), {d, Divisors[n]}, {e, Divisors[k]}];
Table[a[n-k, k], {n, nn}, {k, n-1}]
PROG
(PARI) A(n, k) = {sumdiv(n, d, sumdiv(k, e, moebius(d) * moebius(e) * 2^((n/d) * (k/e))))} \\ Andrew Howroyd, Jan 19 2023
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Feb 04 2019
STATUS
approved