A227866 Derived from von Mangoldt matrix sequence.

1, 1, 4, 27, 64, 3125, 288, 823543, 147456, 4251528, 460800, 285311670611, 111974400, 302875106592253, 3251404800, 13436928000, 106542032486400, 827240261886336764177, 1053455155200000, 1978419655660313589123979, 102395841085440000

Offset

0,3

Comments

Since the logarithm of n is given by the limit of Zeta(s)*Sum_{k=1..n} ((1 - (If k mod n = 0 then n else 0))/k^(s - 1)) as s -> 1, it is natural to ask what the von Mangoldt function variant might look like starting from the table A191898, instead of table A167407. - Mats Granvik, Nov 11 2013

Links

Table of n, a(n) for n=0..20.

Formula

a(prime(n)) = A000312(prime(n)).

Mathematica

Clear[nn, t, n, k, i, s]; nn = 20; t[n_, 1] = 1; t[1, k_] = 1; t[n_, k_] := t[n, k] = If[n >= k, -Sum[t[n - i, k], {i, 1, k - 1}], -Sum[t[k - i, n], {i, 1, n - 1}]]; Exp[Table[Limit[Zeta[s]*Sum[If[n == 1, 0, t[n, k]]/k^(s - 1), {k, 1, n}], s -> 1], {n, 0, nn}]]*(Range[nn + 1] - 1)!

Crossrefs

Cf. A000312, A036505, A177885.

Sequence in context: A058067 A294038 A175701 * A356814 A180576 A158186

Adjacent sequences: A227863 A227864 A227865 * A227867 A227868 A227869

Keyword

nonn

Author

Mats Granvik, Nov 02 2013

Status

approved