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Decimal expansion of the value of the Dickman function at phi + 1 = phi^2 = (3 + sqrt(5))/2 (A104457).
1

%I #13 Jan 09 2025 10:14:32

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

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

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

%N Decimal expansion of the value of the Dickman function at phi + 1 = phi^2 = (3 + sqrt(5))/2 (A104457).

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

%H Pieter Moree, A special value of Dickman's function, Math. Student, Vol. 64 (1995), pp. 47-50; <a href="https://schoolbooksarchive.azimpremjiuniversity.edu.in/handle/20.500.12497/11803">entire volume</a>.

%H Pieter Moree, <a href="https://doi.org/10.1016/j.indag.2013.03.004">Nicolaas Govert de Bruijn, the enchanter of friable integers</a>, Indagationes Mathematicae, Vol. 24, No. 4 (2013), pp. 774-801.

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

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

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

%e 0.10464776377316485385416972771819339482414269115729...

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

%o (PARI) my(phi = quadgen(5)); 1 - 2*log(phi) + log(phi)^2 - Pi^2/60 \\ _Amiram Eldar_, Jan 09 2025

%Y Cf. A000796, A001622, A002390, A013661, A104457, A344476.

%Y Cf. A175475, A244009 (value at 1/2), A245238, A309638.

%K nonn,cons

%O 0,3

%A _Amiram Eldar_, May 20 2021

%E More terms from _Amiram Eldar_, Jan 09 2025