A344476 - OEIS

%I #4 May 21 2021 04:15:59

%S 5,6,0,9,3,8,6,3,9,6,9,2,7,7,1,6,3,3,4,6,0,0,4,1,1,6,3,6,8,0,5,5,6,9,

%T 9,2,9,6,1,1,3,1,7,9,7,0,4,9,6,4,3,9,1,5,0,0,8,1,4,2,3,3,5,1,5,3,3,9,

%U 9,3,9,9,8,5,0,1,7,7,3,7,7,4,4,7,2,9,4

%N Decimal expansion of the value of the Buchstab function at phi + 2 = (5 + sqrt(5))/2 (A296184).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 286.

%D Pieter Moree, A special value of Dickman's function, Math. Student, Vol. 64 (1995), pp. 47-50.

%H A. A. Bukhstab, <a href="http://mi.mathnet.ru/msb5649">Asymptotic estimates of a general number-theoretic function</a> (in Russian), Matematicheskii Sbornik, Vol. 44, No. 6 (1937) pp. 1239-1246.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BuchstabFunction.html">Buchstab Function</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Buchstab_function">Buchstab function</a>.

%F Equals (1 + 2*log(phi) + log(phi)^2 - Pi^2/60)/(phi+2) (Moree, 1995).

%e 0.56093863969277163346004116368055699296113179704964...

%t RealDigits[(1 + 2*Log[GoldenRatio] + Log[GoldenRatio]^2 - Pi^2/60)/(GoldenRatio + 2), 10, 100][[1]]

%Y Cf. A000796, A001622, A002390, A013661, A296184, A344475.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 20 2021