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A227866 Derived from von Mangoldt matrix sequence. 0
1, 1, 4, 27, 64, 3125, 288, 823543, 147456, 4251528, 460800, 285311670611, 111974400, 302875106592253, 3251404800, 13436928000, 106542032486400, 827240261886336764177, 1053455155200000, 1978419655660313589123979, 102395841085440000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Since the logarithm of n is given by the limit of Zeta(s)*Sum from k=1 to n of ((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: A097792 A058067 A175701 * A158186 A272858 A272818

Adjacent sequences:  A227863 A227864 A227865 * A227867 A227868 A227869

KEYWORD

nonn

AUTHOR

Mats Granvik, Nov 02 2013

STATUS

approved

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Last modified May 24 21:22 EDT 2017. Contains 287008 sequences.