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A284748
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Decimal expansion of the sum of reciprocals of composite powers.
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0
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2, 2, 6, 8, 4, 3, 3, 3, 0, 9, 5, 0, 2, 0, 4, 8, 7, 2, 1, 3, 5, 6, 3, 2, 5, 4, 0, 1, 4, 4, 0, 5, 7, 6, 0, 4, 3, 8, 1, 2, 5, 8, 6, 6, 3, 9, 1, 6, 8, 1, 3, 9, 5, 1, 6, 8, 8, 9, 9, 3, 9, 3, 2, 6, 4, 3, 2, 9, 0, 9, 7, 1, 5, 1, 0, 7, 6, 6, 6, 0, 2, 1, 6, 6, 2, 0, 1, 2, 4, 1, 1, 7, 6, 6, 7, 9, 1, 8, 1, 6, 7, 1, 0, 6, 2, 1
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals Sum_(n>=2} Zeta(n) - PrimeZeta(n) - 1 = Sum_(n>=2} CompositeZeta(n).
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EXAMPLE
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Equals 1/(4*3)+1/(6*5)+1/(8*7)+1/(9*8)+1/(10*9)+...
= 0.226843330950204872135632540144057604...
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MATHEMATICA
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RealDigits[ NSum[Zeta[n]-1-PrimeZetaP[n], {n, 2, Infinity}], 10, 105] [[1]]
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PROG
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(PARI) 1 - sumeulerrat(1/(p*(p-1))) \\ Amiram Eldar, Mar 18 2021
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CROSSREFS
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Decimal expansion of the sum of reciprocal powers: A136141 (primes), A154945 (primes at even powers), A152447 (semiprimes), A154932 (squarefree semiprimes).
Decimal expansion of the 'nonprime Zeta function': A275647 (at 2), A278419 (at 3).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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