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A248003
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a(n) = (sum of totatives of n ) / (2^(omega(n)-1)); a(n) = A023896(n) / A007875(n).
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2
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1, 1, 3, 4, 10, 3, 21, 16, 27, 10, 55, 12, 78, 21, 30, 64, 136, 27, 171, 40, 63, 55, 253, 48, 250, 78, 243, 84, 406, 30, 465, 256, 165, 136, 210, 108, 666, 171, 234, 160, 820, 63, 903, 220, 270, 253, 1081, 192, 1029, 250, 408, 312, 1378, 243, 550, 336
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) is multiplicative with a(p^e) = (p-1)*p^(2e-1)/2.
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 2*p/((p-1)^2 * (p+1))) = 3.96555686901754604330173765246769123681199917183404752314230450571038281... - Vaclav Kotesovec, Sep 20 2020
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EXAMPLE
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MATHEMATICA
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Join[{1}, Table[(n/2)*EulerPhi[n]*2^(1 - PrimeNu[n]), {n, 2, 50}]] (* G. C. Greubel, May 22 2017 *)
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PROG
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(Magma) [(n*EulerPhi(n)/2)/(2^((#(PrimeDivisors(n)))-1)): n in [1..100]]
(PARI) concat([1], for(n=2, 50, print1((n/2)*eulerphi(n)*2^(1-omega(n)), ", "))) \\ G. C. Greubel, May 22 2017
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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