A157292 Decimal expansion of 315/(2*Pi^4).

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

Offset: 1

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• easy
• nonn

Comments

Equals the asymptotic mean of the abundancy index of the 5-free numbers (numbers that are not divisible by a 5th power other than 1) (Jakimczuk and Lalín, 2022). - Amiram Eldar, May 12 2023

Examples

			1.61689220511... = (1+1/2^2+1/2^4)*(1+1/3^2+1/3^4)*(1+1/5^2+1/5^4)*(1+1/7^2+1/7^4)*...
		

Links

• Rafael Jakimczuk and Matilde Lalín, Asymptotics of sums of divisor functions over sequences with restricted factorization structure, Notes on Number Theory and Discrete Mathematics, Vol. 28, No. 4 (2022), pp. 617-634, eq. (1).
• Index entries for transcendental numbers.

Crossrefs

Cf. A001248, A004709, A030514, A092744, A013661, A013664, A082020.

Programs

Maple

evalf(315/2/Pi^4) ;

Mathematica

RealDigits[N[Zeta[2]/Zeta[6], 150]][[1]] (* Geoffrey Critzer, Feb 16 2015 *)

PARI

315/2/Pi^4 \\ Charles R Greathouse IV, Oct 01 2022

Formula

Equals Product_{p = primes} (1 + 1/p^2 + 1/p^4), whereas, the product over (1 + 2/p^2 + 1/p^4) equals A082020^2.

Equals A013661/A013664 = Product_{i>=1} (1+1/A001248(i)+1/A030514(i)).

Equals 315*A092744/2.

Equals Sum_{n>=1} 1/A004709(n)^2. - Geoffrey Critzer, Feb 16 2015