A284748 Decimal expansion of the sum of reciprocals of composite powers.

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

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,changed

Author

Terry D. Grant, Apr 01 2017

Extensions

More digits from Vaclav Kotesovec, Jan 13 2021

Status

approved