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| A057794
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(Integer nearest R(10^n)) - pi(10^n), where pi(x) is the number of primes <= x, R(x) = Sum_{ k>=1 } (mu(k)/k * li(x^(1/k))) and li(x) is the Cauchy principal value of the integral from 0 to x of dt/log(t).
(history;
published version)
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#32 by Alois P. Heinz at Tue Apr 13 19:03:38 EDT 2021
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#31 by Eduard Roure Perdices at Tue Apr 13 16:09:22 EDT 2021
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#30 by Eduard Roure Perdices at Tue Apr 13 16:06:53 EDT 2021
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| DATA
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1, 1, 0, -2, -5, 29, 88, 97, -79, -1828, -2318, -1476, -5773, -19200, 73218, 327052, -598255, -3501366, 23884333, -4891825, -86432204, -127132665, 1033299853, -1658989719, -1834784714, -17149335456, -17535487934, -174760519827
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| EXTENSIONS
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Terms a(25)-a(28) obtained using A006880. - Eduard Roure Perdices, Apr 13 2021
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| STATUS
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approved
editing
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#29 by Peter Luschny at Sun Feb 24 16:29:35 EST 2019
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#28 by Georg Fischer at Sun Feb 24 14:37:05 EST 2019
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#27 by Georg Fischer at Sun Feb 24 14:36:25 EST 2019
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| REFERENCES
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Anatolii A. Karatsuba and Ekatherina A. Karatsuba, The "problem of remainders" in theoretical physics: "physical zeta" function, http://www.phy.bg.ac.rs/~mphys6/proceedings5/14-KaratsubaKaratsuba.ps.
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| LINKS
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Anatolii A. Karatsuba and Ekatherina A. Karatsuba, <a href="https://web.archive.org/web/20171109081433/http://www.phy.bg.ac.rs/~mphys6/proceedings5/14-KaratsubaKaratsuba.ps">The "problem of remainders" in theoretical physics: "physical zeta" function</a>, 6th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics, 14-23 September 2010, Belgrade, Serbia. [From Internet Archive Wayback Machine]
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| STATUS
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approved
editing
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Discussion
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| Sun Feb 24
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| Georg Fischer: Link repaired like in A057752.
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#26 by Charles R Greathouse IV at Tue Apr 07 10:50:20 EDT 2015
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| LINKS
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Tomás Oliveira e Silva, <a href="http://wwwsweet.ieetaua.pt/~/tos/primes.html">Tables of values of pi(x) and of pi2(x)</a>
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Discussion
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| Tue Apr 07
| 10:50
| OEIS Server: https://oeis.org/edit/global/2404
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#25 by Charles R Greathouse IV at Tue Apr 07 10:48:37 EDT 2015
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| LINKS
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TomasTomás Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/primes.html">Tables of values of pi(x) and of pi2(x)</a>
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Discussion
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| Tue Apr 07
| 10:48
| OEIS Server: https://oeis.org/edit/global/2403
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#24 by T. D. Noe at Tue Feb 26 20:49:34 EST 2013
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#23 by T. D. Noe at Tue Feb 26 20:48:57 EST 2013
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| LINKS
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Vladimir Pletser, <a href="/A057794/b057794.txt">Table of n, a(n) for n = 1..24</a>
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| EXTENSIONS
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Last two terms a(23) and a(24), with Pi(10^n) for n=23 and 24 from A006880, from Vladimir Pletser, Feb 27, 2013
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| STATUS
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proposed
editing
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Discussion
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| Tue Feb 26
| 20:49
| T. D. Noe: Please do not add a b-file when the sequence fits on 3 lines.
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