A157294 Decimal expansion of 1575/Pi^6.

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

Offset: 1

Author

R. J. Mathar, Feb 26 2009

Keywords

• cons
• easy
• nonn

Comments

Equals the asymptotic mean of the abundancy index of the 7-free numbers (numbers that are not divisible by a 7th power other than 1) (Jakimczuk and Lalín, 2022). - Amiram Eldar, May 12 2023

Examples

			1.63825432044096736634149427498... = (1+1/2^2+1/2^4+1/2^6)*(1+1/3^2+1/3^4+1/3^6)*(1+1/5^2+1/5^4+1/5^6)*(1+1/7^2+1/7^4+1/7^6)*...
		

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, A030514, A030516, A082020, A013661, A013666, A092746, A157290.

Programs

Maple

evalf(1575/Pi^6) ;

Mathematica

RealDigits[1575/Pi^6,10,120][[1]] (* Harvey P. Dale, May 26 2019 *)

PARI

1575/Pi^6 \\ Charles R Greathouse IV, Oct 01 2022

Formula

Equals Product_{p = primes = A000040} (1+1/p^2+1/p^4+1/p^6).

Equals A013661/A013666 = A082020*A157290 = Product_{i>=1} (1+1/A001248(i)+1/A030514(i)+1/A030516(i)) = 1575*A092746.