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A157292
Decimal expansion of 315/(2*Pi^4).
8
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
1,2
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
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).
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
EXAMPLE
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)*...
MAPLE
evalf(315/2/Pi^4) ;
MATHEMATICA
RealDigits[N[Zeta[2]/Zeta[6], 150]][[1]] (* Geoffrey Critzer, Feb 16 2015 *)
PROG
(PARI) 315/2/Pi^4 \\ Charles R Greathouse IV, Oct 01 2022
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, Feb 26 2009
STATUS
approved