cp's OEIS Frontend

A090699 Decimal expansion of the Erdos-Szekeres constant zeta(3/2)/zeta(3).

%I A090699 #32 Apr 29 2023 23:02:30
%S A090699 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 A090699 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 A090699 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 A090699 Decimal expansion of the Erdos-Szekeres constant zeta(3/2)/zeta(3).
%C A090699 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 A090699 S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 112-114.
%H A090699 S. W. Golomb, <a href="http://www.jstor.org/stable/2317020">Powerful numbers</a>, Amer. Math. Monthly, Vol. 77 (1970), 848-852.
%H A090699 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 A090699 Product_{p prime} (1+1/p^(3/2)) = zeta(3/2)/zeta(3). - _T. D. Noe_, May 03 2006
%F A090699 Equals lim_{n->oo} (Sum_{k=1..n} A051904(k) - n)/sqrt(n) (Niven, 1969). - _Amiram Eldar_, Jul 11 2020
%e A090699 zeta(3/2)/zeta(3) = 2.17325431251955413823708984...
%t A090699 RealDigits[N[Zeta[3/2]/Zeta[3],150]][[1]] (* _T. D. Noe_, May 03 2006 *)
%o A090699 (PARI) zeta(3/2)/zeta(3) \\ _Michel Marcus_, Oct 06 2017
%Y A090699 Cf. A001694 (powerful numbers), A102834 (nonsquare powerful numbers).
%Y A090699 Cf. A033150, A051904.
%K A090699 cons,nonn
%O A090699 1,1
%A A090699 _Benoit Cloitre_, Jan 14 2004
%E A090699 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 16 2007