A092744 -id:A092744 - 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

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

Original entry on oeis.org

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

R. J. Mathar, Feb 26 2009

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

			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)*...

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

Maple
```
evalf(315/2/Pi^4) ;
```

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

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

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

A179706 Decimal expansion of e^(1/Pi).

Original entry on oeis.org

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

Offset: 1

Bronte Harkaitz (bronteharkaitz(AT)yahoo.com), Jul 25 2010

			e^(1/Pi) = 1.37480222743935863178...
1.3748022274... = 1 + A049541 + A092742/2! + A092743/3! + A092744/4! + A092745/5! + ... - _R. J. Mathar_, Jul 28 2010

Karl V. Keller, Jr., Table of n, a(n) for n = 1..1000

Cf. A001113 (decimal expansion of e, Euler's number), A000796 (decimal expansion of Pi).

x := exp(1)^(1/Pi) ; x := evalf(x) ; # R. J. Mathar, Jul 28 2010

RealDigits[N[E^(1/Pi),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

log(this number) = A049541. - R. J. Mathar, Jul 28 2010

Edited and extended by Klaus Brockhaus, Jul 29 2010

More digits from R. J. Mathar, Jul 28 2010

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A092742 Decimal expansion of 1/Pi^2.

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

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A179706 Decimal expansion of e^(1/Pi).

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