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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
OFFSET
0,1
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
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
KEYWORD
nonn,cons
AUTHOR
Terry D. Grant, Apr 01 2017
EXTENSIONS
More digits from Vaclav Kotesovec, Jan 13 2021
STATUS
approved