A092746 -id:A092746 - cp's OEIS frontend

A092742 Decimal expansion of 1/Pi^2.

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

Offset: 0

Mohammad K. Azarian, Apr 12 2004

The asymptotic density of squarefree numbers that are divisible by 5. - Amiram Eldar, Mar 25 2021

			0.101321183642337771443879463209727638904358774672246548845609...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 3.6.1, p. 220.

S. Ramanujan, Some formulas in the analytic theory of numbers Messenger of Mathematics, XLV, 1916, pp. 81-84, Formula (3).
Index entries for transcendental numbers

Cf. A000796 (Pi), A002388 (Pi^2), A091925 (Pi^3), A092425 (Pi^4), A092731 (Pi^5), A092732 (Pi^6), A092735 (Pi^7), A092736 (Pi^8).

Cf. A049541 (1/Pi), A092743 (1/Pi^3), A092744 (1/Pi^4), A092745 (1/Pi^5), A092746 (1/Pi^6), A092747 (1/Pi^7), A092748 (1/Pi^8).

RealDigits[N[1/Pi^2,200]][[1]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *) (* Corrected by Harvey P. Dale, Sep 21 2024. *)
realDigitsRecip[Pi^2] (* The realDigitsRecip program is at A021200 *) (* Harvey P. Dale, Sep 21 2024 *)

c=Pi^-2; a=eval(vecextract(Vec(Str(c)),"3..-2"))  \\ M. F. Hasler, Sep 16 2011

A157294 Decimal expansion of 1575/Pi^6.

Original entry on oeis.org

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

R. J. Mathar, Feb 26 2009

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

			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)*...

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.

Cf. A001248, A030514, A030516, A082020, A013661, A013666, A092746, A157290.

Maple
```
evalf(1575/Pi^6) ;
```

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

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

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.

A157295 Decimal expansion of 630/Pi^6.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Feb 26 2009

			0.655301728176386946536... = (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)*...

Masato Kobayashi, Möbius functions of higher rank and Dirichlet series, arXiv:2108.01822 [math.NT], 2021.
Index entries for transcendental numbers.

Cf. A013661, A013662, A013666, A001248, A030514, A030516, A092746, A363551.

Maple
```
evalf(630/Pi^6) ;
```

RealDigits[630/Pi^6, 10, 120][[1]] (* Amiram Eldar, Jun 10 2023 *)

PARI
```
630/Pi^6 \\ Michel Marcus, Aug 05 2021
```

Equals Product_{p primes = A000040} (1-1/p^2+1/p^4-1/p^6).
Equals A013662/(A013661*A013666).
Equals Product_{i>=1} (1-1/A001248(i)+1/A030514(i)-1/A030516(i)).
Equals 630*A092746.
Equals Sum_{n>=1} A363551(n)/n^2. - Amiram Eldar, Jun 10 2023

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A092742 Decimal expansion of 1/Pi^2.

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A157294 Decimal expansion of 1575/Pi^6.

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A157295 Decimal expansion of 630/Pi^6.

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