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A157296
Decimal expansion of 31185/(2*Pi^8).
2
1, 6, 4, 3, 2, 9, 9, 6, 8, 1, 8, 5, 7, 0, 9, 9, 9, 9, 2, 2, 7, 7, 4, 8, 0, 1, 8, 0, 1, 2, 9, 1, 4, 9, 7, 8, 4, 6, 0, 8, 2, 8, 7, 5, 8, 4, 4, 5, 7, 2, 3, 5, 0, 9, 8, 5, 9, 5, 8, 3, 4, 5, 0, 5, 1, 6, 4, 3, 2, 8, 6, 4, 8, 1, 2, 4, 5, 5, 1, 7, 4, 9, 5, 3, 7, 5, 1, 3, 7, 4, 2, 3, 7, 6, 5, 4, 9, 2, 9, 5, 6, 5, 8, 2, 8
OFFSET
1,2
COMMENTS
Equals the asymptotic mean of the abundancy index of the 9-free numbers (numbers that are not divisible by a 9th 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 = A000040} (1+1/p^2+1/p^4+1/p^6+1/p^8). The variant Product_{p} (1+1/p^2+1/p^6+1/p^8) equals A082020*Product_{p} (1+1/p^6) = A082020*zeta(6)/zeta(12) = 10135125/(691*Pi^8).
Equals A013661/A013668 = Product_{i>=1} (1+1/A001248(i)+1/A030514(i)+1/A030516(i)+1/A030514(i)^2) = 15592.5*A092748.
EXAMPLE
1.64329968185709999227... = (1+1/2^2+1/2^4+1/2^6+1/2^8)*(1+1/3^2+1/3^4+1/3^6+1/3^8)*(1+1/5^2+1/5^4+1/5^6+1/5^8)*...
MAPLE
evalf(31185/2/Pi^8) ;
MATHEMATICA
RealDigits[31185/(2*Pi^8), 10, 120][[1]] (* Harvey P. Dale, Mar 30 2018 *)
PROG
(PARI) 31185/2/Pi^8 \\ Charles R Greathouse IV, Oct 01 2022
KEYWORD
cons,easy,nonn
AUTHOR
R. J. Mathar, Feb 26 2009
STATUS
approved