OFFSET
1,3
LINKS
FORMULA
G.f. of column k: Sum_{j>=1} mu(j)^2*PolyLog(-k,x^j), where PolyLog() is the polylogarithm function.
A(n,k) = Sum_{d|n} mu(n/d)^2*d^k.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
2, 3, 5, 9, 17, 33, ...
2, 4, 10, 28, 82, 244, ...
2, 6, 20, 72, 272, 1056, ...
2, 6, 26, 126, 626, 3126, ...
4, 12, 50, 252, 1394, 8052, ...
MATHEMATICA
Table[Function[k, n^k Product[1 + Boole[PrimeQ[d]]/d^k, {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
Table[Function[k, SeriesCoefficient[Sum[MoebiusMu[j]^2 PolyLog[-k, x^j], {j, 1, n}], {x, 0, n}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
Table[Function[k, Sum[MoebiusMu[n/d]^2 d^k, {d, Divisors[n]}]][i - n], {i, 0, 11}, {n, 1, i}] // Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ilya Gutkovskiy, Oct 25 2018
STATUS
approved