A013662 -id:A013662 - cp's OEIS frontend

A007410 Numerator of Sum_{k=1..4} k^(-4).

1, 17, 1393, 22369, 14001361, 14011361, 33654237761, 538589354801, 43631884298881, 43635917056897, 638913789210188977, 638942263173398977, 18249420414596570742097, 18249859383918836502097, 18250192489014819937873

Offset: 1

N. J. A. Sloane, Mira Bernstein

p divides a(p-1) for prime p > 5. p divides a((p-1)/2) for prime p > 5. p^2 divides a((p-1)/2) for prime p = 31, 37. - Alexander Adamchuk, Jul 07 2006
p^2 divides a(p-1) for prime p = 37. - Alexander Adamchuk, Nov 07 2006
Denominators are A007480. See the W. Lang link under A103345 for the rationals and more.
The limit of the rationals Zeta(n) := Sum_{k=1..n} 1/k^4 as n -> infinity is (Pi^4)/90, which is approximately 1.082323234. See A013662.

D. Y. Savio, E. A. Lamagna, and S.-M. Liu, Summation of harmonic numbers, pp. 12-20, in: E. Kaltofen and S. M. Watt, editors, Computers and Mathematics, Springer-Verlag, NY, 1989.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=1..200
Hisanori Mishima, Factorizations of many number sequences.
Hisanori Mishima, Factorizations of many number sequences.

Cf. A001008, A007406, A007408, A007480, A013662.

Numerator[Table[Sum[1/k^4,{k,1,n}],{n,1,20}]] (* Alexander Adamchuk, Jul 07 2006 *)
Accumulate[1/Range[20]^4]//Numerator (* Harvey P. Dale, Jun 28 2020 *)

a(n)=numerator(sum(k=1,n,1/k^4)) \\ Charles R Greathouse IV, Jul 19 2011

Numerators of the coefficients in the expansion of PolyLog(4, x)/(1 - x). - Ilya Gutkovskiy, Apr 10 2017

A013670 Decimal expansion of zeta(12).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

			1.0002460865533080482986379980477396709604160884580034045330409521332520...

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Cf. A013662, A013664, A013666, A013668.

RealDigits[Zeta[12],10,120][[1]] (* Harvey P. Dale, Apr 30 2013 *)

PARI
```
zeta(12) \\ Michel Marcus, Feb 20 2015
```

zeta(12) = 2/3*2^12/(2^12 - 1)*( Sum_{n even} n^2*p(n)/(n^2 - 1)^13 ), where p(n) = 7*n^12 + 182*n^10 + 1001*n^8 + 1716*n^6 + 1001*n^4 + 182*n^2 + 7 is a row polynomial of A091043. - Peter Bala, Dec 05 2013
zeta(12) = Sum_{n >= 1} (A010052(n)/n^6) = Sum {n >= 1} ( (floor(sqrt(n))-floor(sqrt(n-1)))/n^6 ). - Mikael Aaltonen, Feb 20 2015
zeta(12) = 691/638512875*Pi^12 (see A002432). - Rick L. Shepherd, May 30 2016
zeta(12) = Product_{k>=1} 1/(1 - 1/prime(k)^12). - Vaclav Kotesovec, May 02 2020

A092425 Decimal expansion of Pi^4.

Original entry on oeis.org

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

Offset: 2

Mohammad K. Azarian, Mar 22 2004

			97.40909103400243723644033268870511124972758567268542169146785938997085...

Harry J. Smith, Table of n, a(n) for n = 2..20000
Mohammad Reza Yegan, On the irrationality of Pi^4 and Pi^6, Journal of Number Theory, Volume 178, September 2017, Pages 5-10.
Index entries for transcendental numbers

Cf. A000796 (Pi), A002388 (Pi^2), A091925 (Pi^3), A092731 (Pi^5), A092732 (Pi^6), A092735 (Pi^7), A092736 (Pi^8), A058286 (continued fraction), A013662.

R:= RealField(150); (Pi(R))^4; // G. C. Greubel, Mar 09 2018

R:=RealField(110); SetDefaultRealField(R); n:=Pi(R)^4; Reverse(Intseq(Floor(10^98*n))); // Bruno Berselli, Mar 12 2018

RealDigits[Pi^4, 10, 100][[1]] (* G. C. Greubel, Mar 09 2018 *)

default(realprecision, 20080); x=Pi^4/10; for (n=2, 20000, d=floor(x); x=(x-d)*10; write("b092425.txt", n, " ", d)); \\ Harry J. Smith, Jun 22 2009

Equals 120 * Sum_{j>=1} Sum_{i=1..j-1} 1/(i*j)^2. - Enrique Pérez Herrero, Jun 29 2012
Equals Sum_{k>=1} k*(k+1)*(k+2)*zeta(k+3)/2^(k-1). - Amiram Eldar, May 21 2021
From Peter Bala, Oct 21 2023: (Start)
Pi^4 = 90*Sum_{n >= 1} 1/n^4 (Euler).
The following faster converging series representations for the constant Pi^4 may be easily verified using partial fraction expansions of the summands of the series. Presumably, these are the first three cases of an infinite family of similar results.
Let P(n) = n*(n + 1)*(n + 2)/2!. Then Pi^4 = 1575/16 - 15*Sum_{n >= 1} d/dn(P(n))/P(n)^4.
Let Q(n) = n*(n + 1)*(n + 2)*(n + 3)*(n + 4)/4!. Then Pi^4 = 673165/6912 + Sum_{n >= 1} d/dn(Q(n))/Q(n)^4.
Let R(n) = n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n + 5)*(n + 6)/6!. Then Pi^4 = 5610787/57600 - (3/56)*Sum_{n >= 1} d/dn(R(n))/R(n)^4.
Taking 10 terms of the last series gives the approximation Pi^4 = 97.4090910340
  024372(50...), correct to 16 decimal places. (End)

A013680 Continued fraction for zeta(4).

Original entry on oeis.org

1, 12, 6, 1, 3, 1, 4, 183, 1, 1, 2, 1, 3, 1, 1, 5, 4, 2, 7, 23, 1, 1, 1, 1, 3, 2, 4, 2, 2, 22, 1, 13, 5, 1, 4, 2, 1, 3, 1, 1, 1, 6, 11, 40, 1, 7, 5, 2, 4, 1, 2, 3, 14, 9, 1, 33, 78, 1, 12, 4, 1, 2, 551, 1, 1, 1, 1, 1, 1, 2, 1, 9, 2, 7, 3, 1, 3, 2, 15, 1, 1, 2, 2

Offset: 0

N. J. A. Sloane

			zeta(4) = 1 + 1/(12 + 1/(6 + 1/(1 + 1/(3 + ...)))). - _Harry J. Smith_, Apr 29 2009

T. D. Noe, Table of n, a(n) for n = 0..9999
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for zeta function

Cf. A013662 (zeta(4)). - Harry J. Smith, Apr 29 2009

Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013681-A013696.

ContinuedFraction[Zeta[4],80] (* Harvey P. Dale, Oct 13 2013 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^4/90); for (n=1, 20000, write("b013680.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 29 2009

Offset changed by Andrew Howroyd, Jul 09 2024

A215267 Decimal expansion of 90/Pi^4.

Original entry on oeis.org

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

Offset: 0

Jimmy Zotos, Aug 07 2012

Decimal expansion of 1/zeta(4), the inverse of A013662. This is the probability that 4 randomly chosen natural numbers are relatively prime.
Also the asymptotic probability that a random integer is 4-free. See equivalent comments in A088453, A059956. - Balarka Sen, Aug 08 2012
The probability that the greatest common divisor of two numbers selected at random is squarefree (Christopher, 1956). - Amiram Eldar, May 23 2020

			0.92393840292159016702375049404068247276450216682744364463512319...

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 231.

Karl-Heinz Hofmann, Table of n, a(n) for n = 0..10000
John Christopher, The Asymptotic Density of Some k-Dimensional Sets, The American Mathematical Monthly, Vol. 63, No. 6 (1956), pp. 399-401.
Math Forums, Probability that a number is composite, Aug 2012.
Index entries for transcendental numbers

Cf. A013662, A046100 (4-free numbers), A059956 (1/zeta(2)).

RealDigits[90/Pi^4, 10, 100][[1]] (* Bruno Berselli, Aug 07 2012 *)

90/%pi^4; /* Balarka Sen, Aug 08 2012 */

90/Pi^4 \\ Charles R Greathouse IV, Aug 07 2012

Reciprocal of A013662.

1/zeta(4) = 90/Pi^4 = Product_{k>=1} (1 - 1/prime(k)^4) = Sum_{n>=1} mu(n)/n^4, a Dirichlet series for the Möbius function mu. See the examples in Apostol, here for s = 4. - Wolfdieter Lang, Aug 07 2019

A059358 Coefficients in expansion of Sum_{n >= 1} x^n/(1-x^n)^4.

Original entry on oeis.org

0, 1, 5, 11, 25, 36, 71, 85, 145, 176, 260, 287, 455, 456, 649, 726, 961, 970, 1376, 1331, 1820, 1866, 2315, 2301, 3175, 2961, 3736, 3830, 4729, 4496, 5966, 5457, 6945, 6842, 8114, 7890, 10196, 9140, 11215, 11126, 13420, 12342, 15730, 14191, 17515, 17106, 19601

Offset: 0

N. J. A. Sloane, Jan 27 2001

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000

Cf. A000203, A000292, A001157, A001158, A002129, A007437, A013662, A048272, A073570, A101289.

a:= proc(n) option remember;
      add(d*(d+1)*(d+2)/6, d=numtheory[divisors](n))
    end:
seq(a(n), n=0..60);  # Alois P. Heinz, Jun 12 2023

With[{nn=50},CoefficientList[Series[Sum[x^n/(1-x^n)^4,{n,nn}],{x,0,nn}],x]] (* Harvey P. Dale, May 14 2013 *)

a(n) = if(n==0, 0, sumdiv(n, d, binomial(d+2, 3))); \\ Seiichi Manyama, Apr 19 2021

a(n) = if(n==0, 0, my(f = factor(n)); (sigma(f, 3) + 3*sigma(f, 2) + 2 * sigma(f)) / 6); \\ Amiram Eldar, Dec 29 2024

a(n) = (1/6)*(sigma_3(n) + 3*sigma_2(n) + 2*sigma_1(n)), i.e., this sequence is the inverse Möbius transform of tetrahedral (or pyramidal) numbers: n*(n+1)(n+2)/6 with g.f. 1/(1-x)^4 (cf. A000292). - Vladeta Jovovic, Aug 31 2002
L.g.f.: -log(Product_{k>=1} (1 - x^k)^((k+1)*(k+2)/6)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 21 2018
From Amiram Eldar, Dec 29 2024: (Start)
Dirichlet g.f.: zeta(s) * (zeta(s-3) + 3*zeta(s-2) + 2*zeta(s-1)) / 6.
Sum_{k=1..n} a(k) ~ (zeta(4)/24) * n^4. (End)

A098198 Decimal expansion of Pi^4/36 = zeta(2)^2.

Original entry on oeis.org

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

Offset: 1

Labos Elemer, Sep 21 2004

			2.70580808427784547879000924135291975693687737979... = 2*A152649 = A013661^2.

Ce Xu and Jianqiang Zhao, Sun's Three Conjectures on Apéry-like Sums Involving Harmonic Numbers, arXiv:2203.04184 [math.NT], 2022.
Index entries for transcendental numbers

Cf. A002088, A024916.

Mathematica
```
RealDigits[N[Pi^4/36, 256]]
```

zeta(2)^2 \\ Charles R Greathouse IV, Aug 08 2013

Decimal expansion of limit of q(n)= A024916(n)/A002088(n) = SummatorySigma / SummatoryTotient.
Equals Sum_{n>=1} A000005(n)/n^2. - R. J. Mathar, Dec 18 2010
Equals 10*Sum_{n>=2} (psi(n)+gamma)/n^3. - Jean-François Alcover, Feb 25 2013
Equals Zeta(4)*10/4 = A013662/0.4 = 1/A227929. - R. J. Mathar, Jul 20 2025
Equals 10 * zeta(3,1) = 10 * Sum_{n >= 1} 1/n Sum_{k >= n+1} 1/k^3 = 10 * Sum_{n >= 1} 1/n^3 * Sum_{k = 1..n-1} 1/k. - Peter Bala, Aug 07 2025

A120296 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^4.

Original entry on oeis.org

1, 15, 1231, 19615, 12280111, 4090037, 9824498837, 157151464517, 38193952437631, 7637983935923, 111835788321880643, 111830093529238643, 3194097388508809394723, 3194009594644356242723, 15970381078317764649391

Offset: 1

Alexander Adamchuk, Jul 10 2006

p divides a(p-1) for prime p > 2 - similar to Wolstenholme's theorem for A007406(n) (= numerator of Sum_{k=1..n} 1/k^2) and for A007410(n) (= numerator of Sum_{k=1..n} 1/k^4).

Lim_{n -> infinity} a(n)/A334585(n) = A267315 = (7/8)*A013662. - Petros Hadjicostas, May 07 2020

			The first few fractions are 1, 15/16, 1231/1296, 19615/20736, 12280111/12960000, 4090037/4320000, 9824498837/10372320000, ... = A120296/A334585. - _Petros Hadjicostas_, May 06 2020

Cf. A007406, A007410, A013662, A119682, A267315, A334585 (denominators).

Numerator[Table[Sum[(-1)^(k+1)/k^4,{k,1,n}],{n,1,20}]]

a(n) = numerator(sum(k=1, n, (-1)^(k+1)/k^4)); \\ Michel Marcus, May 07 2020

a(n) = numerator(Sum_{k=1..n} (-1)^(k+1)/k^4).

Name edited by Petros Hadjicostas, May 07 2020

A062775 Number of Pythagorean triples mod n: total number of solutions to x^2 + y^2 = z^2 mod n.

Original entry on oeis.org

1, 4, 9, 24, 25, 36, 49, 96, 99, 100, 121, 216, 169, 196, 225, 448, 289, 396, 361, 600, 441, 484, 529, 864, 725, 676, 891, 1176, 841, 900, 961, 1792, 1089, 1156, 1225, 2376, 1369, 1444, 1521, 2400, 1681, 1764, 1849, 2904, 2475, 2116, 2209, 4032, 2695, 2900

Offset: 1

Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 18 2001

a(n) is multiplicative and, for a prime p, a(p) = p^2. Hence a(n) = n^2 if n is squarefree.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe, terms 1001..5000 from Seiichi Manyama)
Gottfried Helms, Pythagorean triples mod n / Solution enhanced, newsgroup sci.math.research, 2003.
László Tóth, Counting solutions of quadratic congruences in several variables revisited,arXiv:1404.4214 [math.NT], 2014.
László Tóth, Counting Solutions of Quadratic Congruences in Several Variables Revisited, J. Int. Seq. 17 (2014), Article 14.11.6.
Index to sequences related to sums of squares.

Cf. A091143 (number of solutions to x^2 + y^2 = z^2 mod 2^n).
Cf. A060968, A087687, A002117, A013662.
Number of solutions to x^k + y^k = z^k mod n: this sequence (k=2), A063454 (k=3), A288099 (k=4), A288100 (k=5), A288101 (k=6), A288102 (k=7), A288103 (k=8), A288104 (k=9), A288105 (k=10).

A062775 := proc(n)
    a := 1;
    for pe in ifactors(n)[2] do
        p := op(1,pe) ;
        e := op(2,pe) ;
        if p = 2 then
            if type(e,'odd') then
                a := a*p^((3*e+1)/2)*(2^((e+1)/2)-1) ;
            else
                a := a*p^(3*e/2)*(2^(e/2+1)-1) ;
            end if;
        else
            if type(e,'odd') then
                a := a*p^((3*e-1)/2)*(p^((e+1)/2)+p^((e-1)/2)-1) ;
            else
                a := a*p^(3*e/2-1)*(p^(e/2+1)+p^(e/2)-1) ;
            end if;
        end if;
    end do:
    a ;
end proc:
seq(A062775(n),n=1..100) ; # R. J. Mathar, Jun 25 2018

Table[cnt=0; Do[If[Mod[x^2+y^2-z^2, n]==0, cnt++ ], {x, 0, n-1}, {y, 0, n-1}, {z, 0, n-1}]; cnt, {n, 50}]
f[p_, e_] := If[OddQ[e], p^(3*(e+1)/2 - 2)*(p^((e+1)/2) + p^((e-1)/2) - 1), p^(3*e/2 - 1) * (p^(e/2 + 1) + p^(e/2) - 1)]; f[2, e_] := If[OddQ[e], 2^(3*(e+1)/2 - 1)*(2^((e+1)/2) - 1), 2^(3*e/2)*(2^(e/2+1)-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Oct 18 2022 *)

a(n) is multiplicative. For the powers of primes p, there are four cases. For p=2, there are cases for even and odd powers: a(2^(2k-1)) = 2^(3k-1) (2^k-1) and a(2^(2k)) = 2^(3k) (2^(k+1)-1). Similarly, for odd primes p, a(p^(2k-1)) = p^(3k-2) (p^k+p^(k-1)-1) and a(p^(2k)) = p^(3k-1) (p^(k+1)+p^k-1). - T. D. Noe, Dec 22 2003
From  Gottfried Helms, May 13 2004: (Start)
If the canonical form of n is n = 2^i * 3^j * 5^k *... * p^q, then it appears that a(n) = n * f(2, i) * f(3, j) * f(5, k) * ... * f(p, q), where f(p, 1) = p for any prime p; f(2, i) = 2^i + 2^i - 2^ceiling(i/2); f(p, i) = p^i + p^(i-1) - p^floor((i-1)/2) for any odd prime p.
For example, a(7) = 49 because a(7) = 7*f(7, 1) = 7*7; a(16) = 448 because a(16) = a(2^4) = 16 * f(2, 4) = 16 * (16+16-4) = 16*28 = 448; a(12) = 216 because a(12) = a(3*2^2) = 12*f(2, 2)*f(3, 1) = 12*(4+4-2)*3 = 216. (End)
Sum_{k=1..n} a(k) ~ c * n^3, where c = (16/45) * Product_{p prime} (1 + 1/(p^3 + p^2 + p)) = (16/45)*zeta(3)/zeta(4) = 0.39488943478263044166... . - Amiram Eldar, Oct 18 2022, Nov 30 2023

More terms from Sascha Kurz, Mar 25 2002

A082540 Number of ordered quadruples (a,b,c,d) with gcd(a,b,c,d)=1 (1 <= {a,b,c,d} <= n).

Original entry on oeis.org

1, 15, 79, 239, 607, 1199, 2303, 3823, 6223, 9279, 13919, 19183, 27007, 35743, 47519, 60735, 78719, 97103, 122447, 148527, 181839, 216959, 262543, 306863, 365343, 423855, 495855, 569055, 661679, 748527, 862047, 972191, 1104831, 1237247

Offset: 1

Benoit Cloitre, May 11 2003

nonn

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Column k=4 of A344527.
Cf. A018805, A071778, A082544, A343978.
Cf. A015634.

a(n)=sum(k=1,n,moebius(k)*floor(n/k)^4)

from functools import lru_cache
@lru_cache(maxsize=None)
def A082540(n):
    if n == 0:
        return 0
    c, j = 1, 2
    k1 = n//j
    while k1 > 1:
        j2 = n//k1 + 1
        c += (j2-j)*A082540(k1)
        j, k1 = j2, n//j2
    return n*(n**3-1)-c+j # Chai Wah Wu, Mar 29 2021

a(n) = Sum_{k=1..n} mu(k)*floor(n/k)^4.
a(n) is asymptotic to c*n^4 with c=0.92393....
Lim_{n->infinity} a(n)/n^4 = 1/zeta(4) = A215267 = 90/Pi^4. - Karl-Heinz Hofmann, Apr 11 2021
Lim_{n->infinity} n^4/a(n) =   zeta(4) = A013662 = Pi^4/90. - Karl-Heinz Hofmann, Apr 11 2021
a(n) = n^4 - Sum_{k=2..n} a(floor(n/k)). - Seiichi Manyama, Sep 13 2024

cp's OEIS Frontend

A007410 Numerator of Sum_{k=1..4} k^(-4).

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A013670 Decimal expansion of zeta(12).

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A092425 Decimal expansion of Pi^4.

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Magma

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A013680 Continued fraction for zeta(4).

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A215267 Decimal expansion of 90/Pi^4.

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Maxima

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A059358 Coefficients in expansion of Sum_{n >= 1} x^n/(1-x^n)^4.

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Maple

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A098198 Decimal expansion of Pi^4/36 = zeta(2)^2.

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