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A347227
Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{d|n} mu(d)*mu(n/d)*d^k.
2
1, 1, -2, 1, -3, -2, 1, -5, -4, 1, 1, -9, -10, 2, -2, 1, -17, -28, 4, -6, 4, 1, -33, -82, 8, -26, 12, -2, 1, -65, -244, 16, -126, 50, -8, 0, 1, -129, -730, 32, -626, 252, -50, 0, 1, 1, -257, -2188, 64, -3126, 1394, -344, 0, 3, 4, 1, -513, -6562, 128, -15626, 8052, -2402, 0, 9, 18, -2
OFFSET
1,3
LINKS
FORMULA
Dirichlet g.f. of column k: 1/(zeta(s)*zeta(s-k)).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
-2, -3, -5, -9, -17, -33, ...
-2, -4, -10, -28, -82, -244, ...
1, 2, 4, 8, 16, 32, ...
-2, -6, -26, -126, -626, -3126, ...
4, 12, 50, 252, 1394, 8052, ...
MATHEMATICA
T[n_, k_] := DivisorSum[n, MoebiusMu[#] * MoebiusMu[n/#] * #^k &]; Table[T[n - k + 1, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Amiram Eldar, Aug 24 2021 *)
PROG
(PARI) T(n, k) = sumdiv(n, d, moebius(d)*moebius(n/d)*d^k);
CROSSREFS
Columns k=0..5 give A007427, A046692, A053822, A053825, A053826, A178448.
T(n,n) gives A347251.
Sequence in context: A179314 A204927 A119441 * A322083 A058399 A209434
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Aug 24 2021
STATUS
approved