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

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, 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, 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

Offset: 1

Author

Benoit Cloitre, Jan 14 2004

Keywords

• cons
• nonn

Comments

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.

Examples

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

References

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

Links

• S. W. Golomb, Powerful numbers, Amer. Math. Monthly, Vol. 77 (1970), 848-852.
• Ivan Niven, Averages of Exponents in Factoring Integers, Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.

Crossrefs

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

Cf. A033150, A051904.

Programs

Mathematica

RealDigits[N[Zeta[3/2]/Zeta[3],150]][[1]] (* T. D. Noe, May 03 2006 *)

PARI

zeta(3/2)/zeta(3) \\ Michel Marcus, Oct 06 2017

Formula

Product_{p prime} (1+1/p^(3/2)) = zeta(3/2)/zeta(3). - T. D. Noe, May 03 2006

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

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 16 2007