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A346202
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a(n) = L(n)^2, where L is Liouville's function.
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1
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1, 0, 1, 0, 1, 0, 1, 4, 1, 0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 16, 9, 4, 9, 4, 1, 0, 1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 9, 4, 1, 0, 1, 4, 9, 16, 25, 16, 25, 36, 25, 36, 25, 36, 49, 36, 25, 16, 9, 4, 9, 4, 9, 4, 9, 4, 1, 4, 9, 16, 9, 16, 25, 36, 49, 36, 49, 64, 49
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OFFSET
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1,8
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COMMENTS
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The Riemann Hypothesis is equivalent to the statement that, for every fixed eps > 0, lim_{n->oo} (L(n) / n^(eps + 1/2)) = 0.
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REFERENCES
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Peter Borwein, Stephen Choi, Brendan Rooney, and Andrea Weirathmueller, The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, 2007, page 6, Theorem 1.2.
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LINKS
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FORMULA
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MAPLE
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L:= proc(n) option remember; `if`(n<1, 0,
(-1)^numtheory[bigomega](n)+L(n-1))
end:
a:= n-> L(n)^2:
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MATHEMATICA
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Table[Sum[LiouvilleLambda[n], {n, 1, nn}]^2, {nn, 1, 77}]
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PROG
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a(n) = sum(i=1, n, sum(j=1, n, a008836(i)*a008836(j))) \\ Felix Fröhlich, Jul 10 2021
(Python)
from functools import reduce
from operator import ixor
from sympy import factorint
def A346202(n): return sum(-1 if reduce(ixor, factorint(i).values(), 0)&1 else 1 for i in range(1, n+1))**2 # Chai Wah Wu, Dec 20 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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