The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A084911 Decimal expansion of linear asymptotic constant B in Sum_{k=1..n} 1/A000688(k) = ~B*n + ... 3
 7, 5, 2, 0, 1, 0, 7, 4, 2, 3, 7, 7, 0, 2, 9, 1, 6, 1, 5, 2, 0, 6, 3, 6, 0, 7, 7, 4, 5, 5, 4, 3, 2, 5, 7, 6, 5, 6, 0, 7, 1, 8, 1, 4, 6, 9, 5, 9, 1, 2, 8, 5, 2, 6, 6, 9, 6, 3, 9, 9, 7, 9, 8, 3, 2, 6, 7, 2, 3, 5, 0, 5, 6, 8, 4, 6, 4, 7, 9, 7, 3, 7, 8, 6, 3, 9, 4, 7, 3, 6, 3, 7, 8, 0, 8, 6, 5, 4, 3, 7, 1, 0, 1, 3, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 274. LINKS Table of n, a(n) for n=0..104. Jean-Marie De Koninck and Aleksandar Ivić, Topics in Arithmetical Functions: Asymptotic Formulae for Sums of Reciprocals of Arithmetical Functions and Related Fields, Amsterdam, Netherlands: North-Holland, 1980. See p. 16. László Tóth, Alternating sums concerning multiplicative arithmetic functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1; arXiv preprint, arXiv:1608.00795 [math.NT], 2016. Eric Weisstein's World of Mathematics, Abelian Group. FORMULA Equals Product_{p prime} (1-Sum_{k >= 2} (1/P(k-1)-1/P(k))/p^k), where P(k) is the unrestricted partition function. - Jean-François Alcover, Apr 29 2016, [typo corrected by Vaclav Kotesovec, Mar 05 2024] Equals lim_{n->oo} (1/n) * Sum_{k=1..n} 1/A000688(k). - Amiram Eldar, Oct 16 2020 EXAMPLE 0.7520107423... MATHEMATICA digits = 10; m0 (* initial number of primes *) = 10^6; dm = 2*10^5; PP = PartitionsP; DP[n_] := DP[n] = (1/PP[n - 1] - 1 /PP[n]) // N[#, digits + 5]&; pmax = Prime[1000]; nmax[p_ /; p <= pmax] := nmax[p] = Module[{n}, For[n = 2, n < 1000, n++, If[Abs[1/PP[n - 1] - 1 /PP[n]]/p^n < 10^-100, Return[n]]]]; nmax[p_ /; p > pmax] := nmax[pmax]; s[p_] := Sum[DP[n]/p^n, {n, 2, nmax[p]}] ; f[m_] := f[m] = Product[1 - s[p], {p, Prime[Range[m]]}]; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits + 2][[1]] != RealDigits[f[m - dm], 10, digits + 2][[1]], m = m + dm; Print[m, " ", RealDigits[f[m]]]]; A0 = f[m]; RealDigits[A0, 10, digits][[1]] (* Jean-François Alcover, Apr 29 2016 *) PROG (PARI) default(realprecision, 120); default(parisize, 10000000); prodeulerrat((1-1/p)*(1 + sum(i = 1, 512, 1/(numbpart(i)*p^i)))) \\ Amiram Eldar, Mar 08 2024 CROSSREFS Cf. A000041, A000688, A021002, A084892, A084893, A272339. Sequence in context: A196486 A216853 A272169 * A073742 A071876 A306538 Adjacent sequences: A084908 A084909 A084910 * A084912 A084913 A084914 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Jun 11 2003 EXTENSIONS Data corrected by Jean-François Alcover, Apr 29 2016 a(10) from Vaclav Kotesovec, Mar 07 2024 More terms from Amiram Eldar, Mar 08 2024 STATUS approved

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

Last modified May 21 00:14 EDT 2024. Contains 372720 sequences. (Running on oeis4.)