login
Decimal expansion of the Erdos-Szekeres constant zeta(3/2)/zeta(3).
23

%I #32 Apr 29 2023 23:02:30

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

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

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

%N Decimal expansion of the Erdos-Szekeres constant zeta(3/2)/zeta(3).

%C Let N(x) denotes the number of 2-full integers not exceeding x. Then lim_{x->oo} N(x)/sqrt(x) = zeta(3/2)/zeta(3). Also related to Niven's constant.

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 112-114.

%H S. W. Golomb, <a href="http://www.jstor.org/stable/2317020">Powerful numbers</a>, Amer. Math. Monthly, Vol. 77 (1970), 848-852.

%H Ivan Niven, <a href="https://doi.org/10.1090/S0002-9939-1969-0241373-5">Averages of Exponents in Factoring Integers</a>, Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.

%F Product_{p prime} (1+1/p^(3/2)) = zeta(3/2)/zeta(3). - _T. D. Noe_, May 03 2006

%F Equals lim_{n->oo} (Sum_{k=1..n} A051904(k) - n)/sqrt(n) (Niven, 1969). - _Amiram Eldar_, Jul 11 2020

%e zeta(3/2)/zeta(3) = 2.17325431251955413823708984...

%t RealDigits[N[Zeta[3/2]/Zeta[3],150]][[1]] (* _T. D. Noe_, May 03 2006 *)

%o (PARI) zeta(3/2)/zeta(3) \\ _Michel Marcus_, Oct 06 2017

%Y Cf. A001694 (powerful numbers), A102834 (nonsquare powerful numbers).

%Y Cf. A033150, A051904.

%K cons,nonn

%O 1,1

%A _Benoit Cloitre_, Jan 14 2004

%E Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 16 2007