login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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: A106168 A106166 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 15 11:44 EDT 2021. Contains 345048 sequences. (Running on oeis4.)