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 A284748 Decimal expansion of the sum of reciprocals of composite powers. 0
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..105. FORMULA Equals Sum_{n>=1} 1/A002808(n)^(n+1) = (A275647 - 1) + (A278419 - 1) + ... Equals Sum_{n>=1} 1/A002808(n)*(A002808(n)-1). Equals Sum_(n>=2} Zeta(n) - PrimeZeta(n) - 1 = Sum_(n>=2} CompositeZeta(n). Equals 1 - A136141. EXAMPLE Equals 1/(4*3)+1/(6*5)+1/(8*7)+1/(9*8)+1/(10*9)+... = 0.226843330950204872135632540144057604... MATHEMATICA RealDigits[ NSum[Zeta[n]-1-PrimeZetaP[n], {n, 2, Infinity}], 10, 105] [[1]] PROG (PARI) 1 - sumeulerrat(1/(p*(p-1))) \\ Amiram Eldar, Mar 18 2021 CROSSREFS Cf. A066247, A077761, A179119, A185380. 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). Sequence in context: A106166 A374330 A101343 * A134457 A326479 A306688 Adjacent sequences: A284745 A284746 A284747 * A284749 A284750 A284751 KEYWORD nonn,cons AUTHOR Terry D. Grant, Apr 01 2017 EXTENSIONS More digits from Vaclav Kotesovec, Jan 13 2021 STATUS approved

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Last modified August 7 17:47 EDT 2024. Contains 375017 sequences. (Running on oeis4.)