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A193056 Reciprocals are the complement to logarithm of Riemann zeta. a(1)=0, for n>1: a(n) = A008683(n) + A100995(n). 2
0, 0, 0, 2, 0, 1, 0, 3, 2, 1, 0, 0, 0, 1, 1, 4, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 3, 0, 0, -1, 0, 5, 1, 1, 1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 6, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 4, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
The characteristic function of primes can be computed as: A010051(n) = A100995(n) - sqrt(A100995(n)*a(n)). But the element-wise multiplication of the sequences inside the sqrt, has no known operation or definition in terms of Dirichlet generating functions.
LINKS
FORMULA
a(1)=0, for n > 1: a(n) = A008683(n) + A100995(n).
Dirichlet series generating function of reciprocals: -0/1*(Zeta(s)-1)^1 + 1/2*(Zeta(s)-1)^2 - 2/3*(Zeta(s)-1)^3 + 3/4*(Zeta(s)-1)^4 - ...
Reciprocals of a(n) = first column in the sum of matrix powers: -0/1*A175992^1 + 1/2*A175992^2 - 2/3*A175992^3 + 3/4*A175992^4...
EXAMPLE
The reciprocals of this sequence, defined by the Dirichlet series generating function are: 0/1,0/1,0/1,1/2,0/1,1/1,0/1,1/3,1/2,1/1, 0/1,0/1...
MATHEMATICA
a100995[n_]:=If[PrimePowerQ[n], FactorInteger[n][[1, 2]], 0] (* From Harvey P. Dale *); Table[If[n==1, 0, MoebiusMu[n] + a100995[n]], {n, 100}] (* Indranil Ghosh, May 27 2017 *)
PROG
(PARI) A193056(n) = if(1==n, 0, moebius(n)+isprimepower(n)); \\ Antti Karttunen, May 27 2017
CROSSREFS
Sequence in context: A187495 A187496 A352552 * A244417 A324811 A086780
KEYWORD
sign
AUTHOR
Mats Granvik, Jul 15 2011
EXTENSIONS
Data section extended to 120 terms by Antti Karttunen, May 27 2017
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)