A013662 -id:A013662 - cp's OEIS frontend

A384052 The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a square.

1, 1, 2, 4, 4, 2, 6, 7, 9, 4, 10, 8, 12, 6, 8, 16, 16, 9, 18, 16, 12, 10, 22, 14, 25, 12, 26, 24, 28, 8, 30, 31, 20, 16, 24, 36, 36, 18, 24, 28, 40, 12, 42, 40, 36, 22, 46, 32, 49, 25, 32, 48, 52, 26, 40, 42, 36, 28, 58, 32, 60, 30, 54, 64, 48, 20, 66, 64, 44

Offset: 1

Amiram Eldar, May 18 2025

Amiram Eldar, Table of n, a(n) for n = 1..10000

Unitary analog of A206369.
Cf. A013662, A350388, A350389, A384046, A384047.
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is: A047994 (1), A384048 (squarefree), A384049 (cubefree), A384050 (powerful), A384051 (cubefull), this sequence (square), A384053 (cube), A384054 (exponentially odd), A384055 (odd), A384056 (power of 2), A384057 (3-smooth), A384058 (5-rough).

f[p_, e_] := p^e - If[OddQ[e], 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a,100]

a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^f[i,2] - if(f[i,2]%2, 1, 0));}

Multiplicative with a(p^e) = p^e-1 if e is odd, and p^e if e is even.
a(n) = n * A047994(n) / A384054(n).
a(n) = A047994(A350389(n)) * A350388(n).
Dirichlet g.f.: zeta(s-1) * zeta(2*s) * Product_{p prime} (1 - 1/p^s - 1/p^(2*s) + 1/p^(2*s-1)).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(4) * Product_{p prime} (1 - 1/p^2 + 1/p^3 - 1/p^4) = 0.74061963657217328604... .

A384054 The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is an exponentially odd number.

Original entry on oeis.org

1, 2, 3, 3, 5, 6, 7, 8, 8, 10, 11, 9, 13, 14, 15, 15, 17, 16, 19, 15, 21, 22, 23, 24, 24, 26, 27, 21, 29, 30, 31, 32, 33, 34, 35, 24, 37, 38, 39, 40, 41, 42, 43, 33, 40, 46, 47, 45, 48, 48, 51, 39, 53, 54, 55, 56, 57, 58, 59, 45, 61, 62, 56, 63, 65, 66, 67, 51

Offset: 1

Amiram Eldar, May 18 2025

Amiram Eldar, Table of n, a(n) for n = 1..10000

Unitary analog of A384041.
Cf. A013662, A268335, A350388, A350389, A384046, A384047.
The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is: A047994 (1), A384048 (squarefree), A384049 (cubefree), A384050 (powerful), A384051 (cubefull), A384052 (square), A384053 (cube), this sequence (exponentially odd), A384055 (odd), A384056 (power of 2), A384057 (3-smooth), A384058 (5-rough).

f[p_, e_] := p^e - If[OddQ[e], 0, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a,100]

a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^f[i,2] - if(f[i,2]%2, 0, 1));}

from math import prod
from sympy import factorint
def A384054(n): return prod(p**e-(e&1^1) for p,e in factorint(n).items()) # Chai Wah Wu, May 21 2025

Multiplicative with a(p^e) = p^e if e is odd, and p^e-1 if e is even.
a(n) = n * A047994(n) / A384052(n).
a(n) = A047994(A350388(n)) * A350389(n).
Dirichlet g.f.: zeta(s-1) * zeta(2*s) * Product_{p prime} (1 - 2/p^(2*s) + 1/p^(3*s-1)).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = zeta(4) * Product_{p prime} (1 - 2/p^4 + 1/p^5) = 0.95692470821076622881... .

A175926 Sum of divisors of cubes.

Original entry on oeis.org

1, 15, 40, 127, 156, 600, 400, 1023, 1093, 2340, 1464, 5080, 2380, 6000, 6240, 8191, 5220, 16395, 7240, 19812, 16000, 21960, 12720, 40920, 19531, 35700, 29524, 50800, 25260, 93600, 30784, 65535, 58560, 78300, 62400, 138811, 52060, 108600, 95200

Offset: 1

Zak Seidov, Oct 19 2010

The Mobius transform of the sequence is 1, 14, 39 ,112, 155,..., which equals the sequence defined by n*A160889(n). - R. J. Mathar, Apr 15 2011

Zhi-Wei Sun noted that the first 10^7 terms are pairwise distinct, but Noam D. Elkies found that a(48142241) = a(48374911), a(384422506) = a(403764207) and so on. - Zhi-Wei Sun, Jan 08 2014

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. sigma(n^k): A000203 (k=1), A065764 (k=2), this sequence (k=3), A202994 (k=4), A203556 (k=5).

Cf. A000578, A013662, A160889.

[ SumOfDivisors(n^3) : n in [1..100]]; // Vincenzo Librandi, Apr 14 2011

DivisorSigma[1,#]&/@((Range[40])^3) (* Harvey P. Dale, Aug 30 2015 *)
f[p_, e_] := (p^(3*e + 1) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Sep 10 2020 *)

a(n) = sigma(n^3); \\ Amiram Eldar, Nov 05 2022

from math import prod
from sympy import factorint
def A175926(n): return prod((p**(3*e+1)-1)//(p-1) for p,e in factorint(n).items()) # Chai Wah Wu, Oct 25 2023

a(n) = A000203(n^3). - R. J. Mathar, Mar 31 2011
Multiplicative with a(p^e) = (p^(3e+1)-1)/(p-1). - R. J. Mathar, Mar 31 2011
Sum_{k>=1} 1/a(k) = 1.11535899887110289127674868460900333554265894187008102863022551119560512446... - Vaclav Kotesovec, Sep 20 2020
Sum_{k=1..n} a(k) ~ c * n^4, where c = (zeta(4)/4) * Product_{p prime} (1 + 1/p^2 + 1/p^3) = 0.4732277044... . - Amiram Eldar, Nov 05 2022

A182448 Decimal expansion of Pi^2/15.

Original entry on oeis.org

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

Offset: 0

Mats Granvik, Apr 29 2012

			0.65797362673929...

Thomas L. Curtright, Bernoulli Partitions, arXiv:2502.09633 [math.CO], 2025. See p. 3. Mentions this sequence.
László Tóth, Linear combinations of Dirichlet series associated with the Thue-Morse sequence, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 22 (2022), #A98; arXiv preprint, arXiv:2211.13570 [math.NT], 2022.
Index entries for transcendental numbers.

Cf. A000796, A008836, A010060, A013661, A013662, A086463, A191898, A249103.

Cf. A347328, A347329, A347330, A347331.

RealDigits[N[Sum[1/(n + 0)^2 - 1/(n + 1)^2 + 1/(n + 2)^2 - 1/(n + 3)^2 - 4/(n + 4)^2 - 1/(n + 5)^2 + 1/(n + 6)^2 - 1/(n + 7)^2 + 1/(n + 8)^2 + 4/(n + 9)^2, {n, 1, Infinity, 10}], 90]][[1]]
RealDigits[N[Sum[LiouvilleLambda[n]/n^2, {n, 1, Infinity}], 90]][[1]]
RealDigits[Pi^2/15,10,120][[1]] (* Harvey P. Dale, May 28 2017 *)

PARI
```
Pi^2/15 \\ Michel Marcus, Oct 21 2014
```

See Mathematica code.
Equals Gamma(4)*zeta(4)/Pi^2 = zeta(4)/zeta(2) = A013662/A013661 = Product_{p prime} (p^2/(p^2+1)). - Stanislav Sykora, Oct 21 2014
Equals (1/10) * Sum_{n >= 0} (-1)^n*( 1/(n + 1/3)^2 - 1/(n + 2/3)^2 ). - Peter Bala, Oct 31 2019
Equals Sum_{k>=1} A008836(k)/k^2. - Amiram Eldar, Jun 23 2020
Equals (1/10) * Sum_{k>=1} (5*t(k-1) + 3*t(k))/k^2, where t(k) = A010060(k) (Tóth, 2022). - Amiram Eldar, Feb 04 2024
Equals 3/5 + (1/5) * Sum_{n>=1} 1/(n^2*(n+1)^2). - Davide Rotondo, May 28 2025
Equals 1/A082020 = A164102/30 = A195055/5. - Hugo Pfoertner, May 28 2025

Offset corrected and more terms added by Rick L. Shepherd, Jan 08 2014

A267315 Decimal expansion of the Dirichlet eta function at 4.

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Jan 13 2016

			eta(4) = 1/1^4 - 1/2^4 + 1/3^4 - 1/4^4 + 1/5^4 - 1/6^4 + ... = 0.9470328294972459175765032344735219149279070829288860...

OEIS Wiki, Euler's alternating zeta function.
Eric Weisstein's World of Mathematics, Dirichlet Eta Function.
Wikipedia, Dirichlet Eta Function.

Cf. A002162, A013662, A072691, A120296, A197070, A334585.

pi:= 7*Pi(RealField(110))^4 / 720; Reverse(Intseq(Floor(10^100*pi))); // Vincenzo Librandi, Feb 04 2016

Mathematica
```
RealDigits[(7 Pi^4)/720, 10, 120][[1]]
```

7*Pi^4/720 \\ Michel Marcus, Feb 01 2016

s = RLF(0); s
RealField(110)(s)
for i in range(1,10000): s += -((-1)^i/((i)^4))
print(s) # Terry D. Grant, Aug 04 2016

eta(4) = Sum_{k > 0} (-1)^(k+1)/k^4 = (7*Pi^4)/720.

eta(4) = Lim_{n -> infinity} A120296(n)/A334585(n) = (7/8)*A013662. - Petros Hadjicostas, May 07 2020

A256919 Decimal expansion of Sum_{k>=1} (zeta(4*k) - 1).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Apr 13 2015

			0.0866629762657094129329746026249997547771718667980916672...
= -3 + Pi^4/90 + Pi^8/9450 + 691*Pi^12/638512875 + ...

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Insights (2011) p. 265.

V. S. Adamchik, H. M. Srivastava, Some series of Zeta and related functions, Analysis (Munich) 18 (2) (1998) 131-144, eq. (2.25).
Eric Weisstein's MathWorld, Riemann Zeta Function
Wikipedia, Riemann Zeta Function

Cf. A013662, A013666, A013670, A175316, A256920, A339529, A339530, A339604 (3k-1).

Join[{0}, RealDigits[7/8 - (Pi/4)*Coth[Pi], 10, 104] // First]

Equals 7/8 - (Pi/4)*coth(Pi).
Equals Sum_{n>=2} 1/(n^4 - 1). - Vaclav Kotesovec, Dec 08 2020
Equals (1/2)* Sum_{n>=2} 1/(n^2-1) - (1/2)* Sum_{n>=2} 1/(n^2+1) = (3/4 - A100554)/2. - R. J. Mathar, Jan 22 2021

A008233 a(n) = floor(n/4)floor((n+1)/4)floor((n+2)/4)*floor((n+3)/4).

Original entry on oeis.org

0, 0, 0, 0, 1, 2, 4, 8, 16, 24, 36, 54, 81, 108, 144, 192, 256, 320, 400, 500, 625, 750, 900, 1080, 1296, 1512, 1764, 2058, 2401, 2744, 3136, 3584, 4096, 4608, 5184, 5832, 6561, 7290, 8100, 9000, 10000, 11000, 12100, 13310, 14641, 15972, 17424, 19008, 20736

Offset: 0

N. J. A. Sloane

a(n) is the maximal product of four nonnegative integers whose sum is n. - Andres Cicuttin, Sep 26 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..3000
Dhruv Mubayi, Counting substructures II: Hypergraphs, preprint, 2012.
Dhruv Mubayi, Counting substructures II: Hypergraphs, Combinatorica 33 (2013), no. 5, 591--612. MR3132928.
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,3,-6,3,0,-3,6,-3,0,1,-2,1).

Maximal product of k positive integers with sum n, for k = 2..10: A002620 (k=2), A006501 (k=3), this sequence (k=4), A008382 (k=5), A008881 (k=6), A009641 (k=7), A009694 (k=8), A009714 (k=9), A354600 (k=10).

Cf. A013662.

a008233 n = product $ map (`div` 4) [n..n+3]
-- Reinhard Zumkeller, Jun 08 2011

[Floor(n/4)*Floor((n+1)/4)*Floor((n+2)/4)*Floor((n+3)/4): n in [0..50]]; // Vincenzo Librandi, Jun 09 2011

A008233:=n->floor(n/4)*floor((n+1)/4)*floor((n+2)/4)*floor((n+3)/4); seq(A008233(n), n=0..50); # Wesley Ivan Hurt, Dec 31 2013

Table[Floor[n/4]*Floor[(n + 1)/4]*Floor[(n + 2)/4]*Floor[(n + 3)/4], {n, 0, 50}] (* Stefan Steinerberger, Apr 03 2006 *)
Table[Times@@Floor[Range[n,n+3]/4],{n,0,50}] (* Harvey P. Dale, Mar 30 2019 *)

a(n) = prod(i=0, 3, (n+i)\4); \\ Altug Alkan, Sep 27 2018

Let b(n) = A002620(n), the quarter-squares. Then this sequence is b(0)*b(0), b(0)*b(1), b(1)*b(1), b(1)*b(2), b(2)*b(2), b(2)*b(3), ...
From R. J. Mathar, Feb 20 2011: (Start)
a(n) = 2*a(n-1) - a(n-2) + 3*a(n-4) - 6*a(n-5) + 3*a(n-6) - 3*a(n-8) + 6*a(n-9) - 3*a(n-10) + a(n-12) - 2*a(n-13) + a(n-14).
G.f.: -x^4*(1+x^6+x^2+2*x^3+x^4) / ( (1+x)^3*(x^2+1)^3*(x-1)^5 ). (End)
Sum_{n>=4} 1/a(n) = 1 + zeta(4). - Amiram Eldar, Jan 10 2023
a(4*n) = n^4. - Bernard Schott, Jan 24 2023

More terms from Stefan Steinerberger, Apr 03 2006

A045823 a(n) = sigma_3(2*n+1).

Original entry on oeis.org

1, 28, 126, 344, 757, 1332, 2198, 3528, 4914, 6860, 9632, 12168, 15751, 20440, 24390, 29792, 37296, 43344, 50654, 61544, 68922, 79508, 95382, 103824, 117993, 137592, 148878, 167832, 192080, 205380, 226982, 260408, 276948, 300764, 340704, 357912

Offset: 0

N. J. A. Sloane

			q + 28*q^3 + 126*q^5 + 344*q^7 + 757*q^9 + 1332*q^11 + 2198*q^13 + ...

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Equals A045819/2.
Bisection of A001158.
Cf. A008438, A013662, A091986.

[DivisorSigma(3, 2*n+1): n in [0..40]]; // Vincenzo Librandi, Jun 02 2019

A045823 := proc(n)
    numtheory[sigma][3](2*n+1) ;
end proc:
seq(A045823(n),n=0..30) ; # R. J. Mathar, Nov 25 2018

DivisorSigma[3, Range[1, 75, 2]] (* Harvey P. Dale, Jan 11 2015 *)

{a(n) = if( n<0, 0, sigma(2 * n + 1, 3))} /* Michael Somos, Nov 29 2007 */

{a(n) = local(A); if( n<0, 0, n *= 2; A = x * O(x^n); polcoeff( (eta(x^2 + A)^24 + eta(x + A)^16 * eta(x^4 + A)^8) / (2 * eta(x + A)^8 * eta(x^2 + A)^8), n))} /* Michael Somos, Nov 29 2007 */

Expansion of q^(-1) * ( E_4(q) - 9 * E_4(q^2) + 8 * E_4(q^4) ) / 240 in powers of q^2. - Michael Somos, Nov 29 2007
Expansion of q^(-1) * (eta(q^2)^24 + eta(q)^16 * eta(q^4)^8) / (2 * eta(q)^8 * eta(q^2)^8) in powers of q^2. - Michael Somos, Nov 29 2007
a(n) = b(2*n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(p^e) = ((p^3)^(e+1) - 1) / (p^3 - 1) if p>2. - Michael Somos, Nov 29 2007
G.f.: (theta_3(q)^8 - theta_4(q)^8) / (32*q) = Sum_{n>=0} sigma_3(2*n+1)*q^(2*n). - Paul D. Hanna, Jun 02 2018
Sum_{k=0..n} a(k) ~ (15*zeta(4)/8) * n^4. - Amiram Eldar, Dec 12 2023

More terms from Benoit Cloitre, Apr 12 2003

A053167 Smallest 4th power divisible by n.

Original entry on oeis.org

1, 16, 81, 16, 625, 1296, 2401, 16, 81, 10000, 14641, 1296, 28561, 38416, 50625, 16, 83521, 1296, 130321, 10000, 194481, 234256, 279841, 1296, 625, 456976, 81, 38416, 707281, 810000, 923521, 256, 1185921, 1336336, 1500625, 1296, 1874161, 2085136

Offset: 1

Henry Bottomley, Feb 29 2000

Amiram Eldar, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.

Cf. A000190, A007913, A008835.

Cf. A013662, A013674.

f[p_, e_] := p^(e + Mod[4 - Mod[e, 4], 4]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019*)

a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^(f[i,2] + (4-f[i,2])%4));} \\ Amiram Eldar, Oct 27 2022

a(n) = (n/A000190(n))^4 = (n*A007913(n))^2/A008835(n*A007913(n)).
From Amiram Eldar, Jul 29 2022: (Start)
Multiplicative with a(p^e) = p^(e + ((4-e) mod 4)).
Sum_{n>=1} 1/a(n) = Product_{p prime} ((p^4+3)/(p^4-1)) = 1.341459051107600424... . (End)
Sum_{k=1..n} a(k) ~ c * n^5, where c = (zeta(16)/(5*zeta(4))) * Product_{p prime} (1 - 1/p^2 + 1/p^4 - 1/p^7 + 1/p^8) = 0.1230279197... . - Amiram Eldar, Oct 27 2022

A300707 Decimal expansion of Pi^4/96.

Original entry on oeis.org

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

Offset: 1

Iaroslav V. Blagouchine, Mar 11 2018

Also the sum of the series Sum_{n>=0} (1/(2n+1)^4), whose value is obtained from zeta(4) given by L. Euler in 1735: Sum_{n>=0} (2n+1)^(-s) = (1-2^(-s))*zeta(s).

For the partial sums of this series see A120269/A128493. - Wolfdieter Lang, Sep 02 2019

			1.0146780316041920545462534655073449088513290174238064...

Eric Weisstein's World of Mathematics, Dirichlet Lambda Function. See (6).
Index entries for transcendental numbers

Cf. A013662, A092425, A111003, A120269, A128493, A300709, A300710, A300731.

MATLAB
```
format long; pi^4/96
```
Maple
```
evalf((1/96)*Pi^4, 120)
```
Mathematica
```
RealDigits[Pi^4/96, 10, 120][[1]]
```
PARI
```
default(realprecision, 120); Pi^4/96
```

Equals A092425/96. - Omar E. Pol, Mar 11 2018
Equals (15/16)*zeta(4) = (15/16)*A013662. - Wolfdieter Lang, Sep 02 2019
Equals Sum_{k>=1} 1/(2*k-1)^4. - Sean A. Irvine, Mar 25 2025
Equals lambda(4), where lambda is the Dirichlet lambda function. - Michel Marcus, Aug 15 2025

cp's OEIS Frontend

A384052 The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is a square.

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A384054 The number of integers k from 1 to n such that the greatest divisor of k that is a unitary divisor of n is an exponentially odd number.

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A175926 Sum of divisors of cubes.

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Magma

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A182448 Decimal expansion of Pi^2/15.

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A267315 Decimal expansion of the Dirichlet eta function at 4.

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A256919 Decimal expansion of Sum_{k>=1} (zeta(4*k) - 1).

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A008233 a(n) = floor(n/4)*floor((n+1)/4)*floor((n+2)/4)*floor((n+3)/4).

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Haskell

A008233 a(n) = floor(n/4)floor((n+1)/4)floor((n+2)/4)*floor((n+3)/4).