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A349136
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Möbius transform of Kimberling's paraphrases, A003602.
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19
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1, 0, 1, 0, 2, 0, 3, 0, 3, 0, 5, 0, 6, 0, 4, 0, 8, 0, 9, 0, 6, 0, 11, 0, 10, 0, 9, 0, 14, 0, 15, 0, 10, 0, 12, 0, 18, 0, 12, 0, 20, 0, 21, 0, 12, 0, 23, 0, 21, 0, 16, 0, 26, 0, 20, 0, 18, 0, 29, 0, 30, 0, 18, 0, 24, 0, 33, 0, 22, 0, 35, 0, 36, 0, 20, 0, 30, 0, 39, 0, 27, 0, 41, 0, 32, 0, 28, 0, 44, 0, 36, 0, 30, 0, 36
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OFFSET
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1,5
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LINKS
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FORMULA
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a(1) = 1, a(n) = A000010(n)/2 for odd n > 1, a(n) = 0 for even n.
Sum_{k=1..n} a(k) ~ (1/Pi^2)*n^2. - Amiram Eldar, Jul 15 2023
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MAPLE
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with(numtheory): a:=proc(n) if n=1 then 1; elif n mod 2 = 0 then 0; else phi(n)/2; fi: end proc: seq(a(n), n=1..60); # Ridouane Oudra, Jul 13 2023
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MATHEMATICA
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k[n_] := (n/2^IntegerExponent[n, 2] + 1)/2; a[n_] := DivisorSum[n, MoebiusMu[#] * k[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 13 2021 *)
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PROG
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(PARI) A349136(n) = if(1==n, 1, if(n%2, eulerphi(n)/2, 0));
(PARI)
A003602(n) = (1+(n>>valuation(n, 2)))/2;
(Python)
from sympy import totient
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CROSSREFS
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Agrees with A055034 on odd arguments.
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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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