A078434 -id:A078434 - cp's OEIS frontend

A078470 Continued fraction for zeta(3/2) (A078434).

2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 22, 209, 2, 1, 15, 25, 2, 1, 11, 1, 1, 5, 8, 2, 2, 20, 1, 4, 1, 2, 3, 3, 2, 1, 2, 2, 5, 1, 1, 2, 195, 1, 1, 1, 1, 1, 27, 27, 1, 45, 4, 5, 1, 2, 82, 1, 1, 2, 1, 6, 6, 1, 8, 1, 2, 1, 17, 3, 8, 1, 4, 1, 1, 2, 4, 8, 6, 2, 3, 6, 2, 2, 5, 2, 3, 5, 1, 5, 9, 1

Offset: 0

Robert G. Wilson v, Jan 01 2003

Cf. A078434 (decimal expansion).

Mathematica
```
ContinuedFraction[ Zeta[3/2], 100]
```

Offset changed by Andrew Howroyd, Aug 07 2024

A033461 Number of partitions of n into distinct squares.

Original entry on oeis.org

1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 2, 3, 1, 1, 4, 3, 0, 1, 2, 2, 1, 0, 1, 4, 3, 0, 2, 4, 2, 1, 3, 2, 1, 2, 3, 3, 2, 1, 3, 6, 3, 0, 2, 5, 3, 0, 1, 3, 3, 3, 4

Offset: 0

N. J. A. Sloane

"WEIGH" transform of squares A000290.
a(n) = 0 for n in {A001422}, a(n) > 0 for n in {A003995}. - Alois P. Heinz, May 14 2014
Number of partitions of n in which each part i has multiplicity i. Example: a(50)=3 because we have [1,2,2,3,3,3,6,6,6,6,6,6], [1,7,7,7,7,7,7,7], and [3,3,3,4,4,4,4,5,5,5,5,5]. - Emeric Deutsch, Jan 26 2016
The Heinz numbers of integer partitions into distinct pairs are given by A324587. - Gus Wiseman, Mar 09 2019
From Gus Wiseman, Mar 09 2019: (Start)
Equivalent to Emeric Deutsch's comment, a(n) is the number of integer partitions of n where the multiplicities (where if x < y the multiplicity of x is counted prior to the multiplicity of y) are equal to the distinct parts in increasing order. The Heinz numbers of these partitions are given by A109298. For example, the first 30 terms count the following integer partitions:
(1)
(22)
(221)
(333)
(3331)
(33322)
(333221)
(4444)
(44441)
(444422)
(4444221)
(55555)
(4444333)
(555551)
(44443331)
(5555522)
(444433322)
(55555221)
(4444333221)
The case where the distinct parts are taken in decreasing order is A324572, with Heinz numbers given by A324571.
(End)

			a(50)=3 because we have [1,4,9,36], [1,49], and [9,16,25]. - _Emeric Deutsch_, Jan 26 2016
From _Gus Wiseman_, Mar 09 2019: (Start)
The first 30 terms count the following integer partitions:
   1: (1)
   4: (4)
   5: (4,1)
   9: (9)
  10: (9,1)
  13: (9,4)
  14: (9,4,1)
  16: (16)
  17: (16,1)
  20: (16,4)
  21: (16,4,1)
  25: (25)
  25: (16,9)
  26: (25,1)
  26: (16,9,1)
  29: (25,4)
  29: (16,9,4)
  30: (25,4,1)
  30: (16,9,4,1)
(End)

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 288-289.

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)
M. Brack, M. V. N. Murthy, and J. Bartel, Application of semiclassical methods to number theory, University of Regensburg (Germany, 2020).
Martin Klazar, What is an answer? — remarks, results and problems on PIO formulas in combinatorial enumeration, part I, arXiv:1808.08449 [math.CO], 2018.
Vaclav Kotesovec, Graph - The asymptotic ratio.
M. V. N. Murthy, Matthias Brack, Rajat K. Bhaduri, and Johann Bartel, Semi-classical analysis of distinct square partitions, arXiv:1808.05146 [cond-mat.stat-mech], 2018.

Cf. A001422, A003995, A078434, A242434 (the same for compositions), A279329.
Cf. A001156 (non-strict case), A001462, A005117, A052335, A078135, A109298, A114638, A117144, A324571, A324572, A324587, A324588.
Row sums of A341040.

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i-1))))
    end:
a:= n-> b(n, isqrt(n)):
seq(a(n), n=0..100);  # Alois P. Heinz, May 14 2014

nn=10; CoefficientList[Series[Product[(1+x^(k*k)), {k,nn}], {x,0,nn*nn}], x] (* T. D. Noe, Jul 24 2006 *)
b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i^2 > n, 0, b[n - i^2, i-1]]]]; a[n_] := b[n, Floor[Sqrt[n]]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Sep 21 2015, after Alois P. Heinz *)
nmax = 20; poly = ConstantArray[0, nmax^2 + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[Do[poly[[j + 1]] += poly[[j - k^2 + 1]], {j, nmax^2, k^2, -1}];, {k, 2, nmax}]; poly (* Vaclav Kotesovec, Dec 09 2016 *)
Table[Length[Select[IntegerPartitions[n],Reverse[Union[#]]==Length/@Split[#]&]],{n,30}] (* Gus Wiseman, Mar 09 2019 *)

a(n)=polcoeff(prod(k=1,sqrt(n),1+x^k^2), n)

first(n)=Vec(prod(k=1,sqrtint(n),1+'x^k^2,O('x^(n+1))+1)) \\ Charles R Greathouse IV, Sep 03 2015

from functools import cache
from sympy.core.power import isqrt
@cache
def b(n,i):
  # Code after Alois P. Heinz
  if n == 0: return 1
  if i == 0: return 0
  i2 = i*i
  return b(n, i-1) + (0 if i2 > n else b(n - i2, i-1))
a = lambda n: b(n, isqrt(n))
print([a(n) for n in range(1, 101)]) # Darío Clavijo, Nov 30 2023

G.f.: Product_{n>=1} ( 1+x^(n^2) ).
a(n) ~ exp(3 * 2^(-5/3) * Pi^(1/3) * ((sqrt(2)-1)*zeta(3/2))^(2/3) * n^(1/3)) * ((sqrt(2)-1)*zeta(3/2))^(1/3) / (2^(4/3) * sqrt(3) * Pi^(1/3) * n^(5/6)), where zeta(3/2) = A078434. - Vaclav Kotesovec, Dec 09 2016
See Murthy, Brack, Bhaduri, Bartel (2018) for a more complete asymptotic expansion. - N. J. A. Sloane, Aug 17 2018

More terms from Michael Somos

A112526 Characteristic function for powerful numbers.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0

Offset: 1

Franklin T. Adams-Watters, Sep 09 2005

A signed multiplicative variant is defined by b(n) = a(n)*mu(n) with mu = A008683, such that b(p^e)=0 if e=1 and b(p^e)= -1 if e>1. This has Dirichlet series Sum_{n>=1} b(n)/n = A005596 and Sum_{n>=1} b(n)/n^2 = A065471. - R. J. Mathar, Apr 04 2011

			a(72) = 1 because 72 = 2^3*3^2 has all exponents > 1.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Powerful Number.
Index entries for characteristic functions.

Differs from characteristic function of perfect powers A075802 at Achilles numbers A052486.
Cf. A001694 (powerful numbers), A124010, A001221, A027746.
Cf. A008683, A008966, A005596, A065471, A082695, A063524.
Cf. A002117, A078434, A005361.

a112526 1 = 1
a112526 n = fromEnum $ (> 1) $ minimum $ a124010_row n
-- Reinhard Zumkeller, Jun 03 2015, Sep 16 2011

cfpn[n_]:=If[n==1||Min[Transpose[FactorInteger[n]][[2]]]>1,1,0]; Array[ cfpn,120] (* Harvey P. Dale, Jul 17 2012 *)

for(n=1, 100, print1(direuler(p=2, n, (1+X^3)/(1-X^2))[n], ", ")) \\ Vaclav Kotesovec, Jul 15 2022

a(n) = ispowerful(n); \\ Amiram Eldar, Jul 02 2025

from sympy import factorint
def A112526(n): return int(all(e>1 for e in factorint(n).values())) # Chai Wah Wu, Sep 15 2024

Multiplicative with a(p^e) = 1 - 0^(e-1), e > 0 and p prime.
Dirichlet g.f.: zeta(2*s)*zeta(3*s)/zeta(6*s), e.g., A082695 at s=1.
a(n) * A008966(n) = A063524(n). - Reinhard Zumkeller, Sep 16 2011
a(n) = {m: Min{A124010(m,k): k=1..A001221(m)} > 1}. - Reinhard Zumkeller, Jun 03 2015
Sum_{k=1..n} a(k) ~ zeta(3/2)*sqrt(n)/zeta(3) + 6*zeta(2/3)*n^(1/3)/Pi^2. - Vaclav Kotesovec, Feb 08 2019
a(n) = Sum_{d|n} A005361(d)*A008683(n/d). - Ridouane Oudra, Jul 03 2025

A059750 Decimal expansion of zeta(1/2) (negated).

Original entry on oeis.org

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

Offset: 1

Peter Walker (peterw(AT)aus.ac.ae), Feb 11 2001

zeta(1/2) can be calculated as a limit similar to the limit for the Euler-Mascheroni constant or Euler gamma. - Mats Granvik Nov 14 2012

The WolframAlpha link gives 3 series and 3 integrals for zeta(1/2). - Jonathan Sondow, Jun 20 2013

			-1.4603545088095868128894991525152980124672293310125814905428860878...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3, p. 43.

Harry J. Smith, Table of n, a(n) for n = 1..5000
B. K. Choudhury, The Riemann zeta-function and its derivatives, Proc. R. Soc. Lond A 445 (1995) 477, Table 3.
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 99.
Fredrik Johansson, zeta(1/2) to 1 million digits.
Fredrik Johansson, Rapid computation of special values of Dirichlet L-functions, arxiv:2110.10583 [math.NA], 2021.
Hisashi Kobayashi, Some results on the xi(s) and Xi(t) functions associated with Riemann's zeta(s) function, arXiv preprint arXiv:1603.02954 [math.NT], 2016.
Lutz Mattner and Irina Shevtsova, An optimal Berry-Esseen type theorem for integrals of smooth functions, arXiv:1710.08503 [math.PR], 2017.
J. Sondow and E. W. Weisstein, MathWorld: Riemann Zeta Function
WolframAlpha, zeta(1/2)

Cf. A161688 (continued fraction), A078434, A014176, A113024.

Maple
```
Digits := 120; evalf(Zeta(1/2));
```

RealDigits[ Zeta[1/2], 10, 111][[1]] (* Robert G. Wilson v, Oct 11 2005 *)
RealDigits[N[Limit[Sum[1/Sqrt[n], {n, 1, k}] - 2*Sqrt[k], k -> Infinity], 90]][[1]] (* Mats Granvik Nov 14 2012 *)

default(realprecision, 5080); x=-zeta(1/2); for (n=1, 5000, d=floor(x); x=(x-d)*10; write("b059750.txt", n, " ", d)); \\ Harry J. Smith, Jun 29 2009

zeta(1/2) = lim_{k->oo} ( Sum_{n=1..k} 1/n^(1/2) - 2*k^(1/2) ) (according to Mathematica 8). - Mats Granvik Nov 14 2012
From Magri Zino, Jan 05 2014 - personal communication: (Start)
The previous result is the case q=2 of the following generalization:
zeta(1/q) = lim_{k->oo} (Sum_{n=1..k} 1/n^(1/q) - (q/(q-1))*k^((q-1)/q)), with q>1. Example: for q=3/2, zeta(2/3) = lim_{k->oo} (Sum_{n=1..k} 1/n^(2/3) - 3*k^(1/3)) = -2.447580736233658231... (End)
Equals -A014176*A113024. - Peter Luschny, Oct 25 2021

Sign of the constant reversed by R. J. Mathar, Feb 05 2009

A183097 a(n) = sum of powerful divisors d (including 1) of n.

Original entry on oeis.org

1, 1, 1, 5, 1, 1, 1, 13, 10, 1, 1, 5, 1, 1, 1, 29, 1, 10, 1, 5, 1, 1, 1, 13, 26, 1, 37, 5, 1, 1, 1, 61, 1, 1, 1, 50, 1, 1, 1, 13, 1, 1, 1, 5, 10, 1, 1, 29, 50, 26, 1, 5, 1, 37, 1, 13, 1, 1, 1, 5, 1, 1, 10, 125, 1, 1, 1, 5, 1, 1, 1, 130, 1, 1, 26, 5, 1, 1, 1, 29, 118, 1, 1, 5, 1, 1, 1, 13, 1, 10, 1, 5, 1, 1, 1, 61, 1, 50, 10, 130

Offset: 1

Jaroslav Krizek, Dec 25 2010

Sequence is not the same as A091051(n); a(72) = 130, A091051(72) = 58.

a(n) = sum of divisors d of n from set A001694 - powerful numbers.

			For n = 12, set of such divisors is {1, 4}; a(12) = 1+4 = 5.

Antti Karttunen, Table of n, a(n) for n = 1..16385
Index entries for sequences related to sums of divisors.

Cf. A001694, A091051, A183102.

Cf. A002117, A078434.

A183097 := proc(n)
    local a,pe,p,e ;
    a := 1;
    for pe in ifactors(n)[2] do
        p := op(1,pe) ;
        e := op(2,pe) ;
        if e > 1 then
            a := a* ( (p^(e+1)-1)/(p-1)-p) ;
        end if;
    end do:
    a ;
end proc: # R. J. Mathar, Jun 02 2020

fun[p_,e_] := (p^(e+1)-1)/(p-1) - p; a[1] = 1; a[n_] := Times @@ (fun @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, May 14 2019 *)

A183097(n) = sumdiv(n, d, ispowerful(d)*d); \\ Antti Karttunen, Oct 07 2017

a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i,1]^(f[i,2]+1)-1) / (f[i,1]-1) - f[i,1]);} \\ Amiram Eldar, Dec 24 2023

a(n) = A000203(n) - A183098(n) = A183100(n) + 1.
a(1) = 1, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = ((p^(k+1)-1) / (p-1))-p, for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.
From Amiram Eldar, Dec 24 2023: (Start)
Dirichlet g.f.: zeta(s) * zeta(2*s-2) * zeta(3*s-3) / zeta(6*s-6).
Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = zeta(3/2)^2/(3*zeta(3)) = 1.892451... . (End)

A358347 a(n) is the sum of the unitary divisors of n that are squares.

Original entry on oeis.org

1, 1, 1, 5, 1, 1, 1, 1, 10, 1, 1, 5, 1, 1, 1, 17, 1, 10, 1, 5, 1, 1, 1, 1, 26, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 50, 1, 1, 1, 1, 1, 1, 1, 5, 10, 1, 1, 17, 50, 26, 1, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 10, 65, 1, 1, 1, 5, 1, 1, 1, 10, 1, 1, 26, 5, 1, 1, 1, 17, 82, 1

Offset: 1

Amiram Eldar, Nov 11 2022

The number of unitary divisors of n that are squares is A056624(n).

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

Cf. A056624, A077610, A078434, A247041, A268335, A350388, A351568.

Similar sequences: A033634, A034448, A035316, A358346.

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

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

a(n) >= 1 with equality if and only if n is an exponentially odd number (A268335).
Multiplicative with a(p^e) = p^e + 1 if e is even, and 1 otherwise.
a(n) = A034448(n)/A358346(n).
Sum_{k=1..n} a(k) ~ c * n^(3/2), where c = zeta(3/2)/(3*zeta(5/2)) = 0.6491241554... .
Dirichlet g.f.: zeta(s)*zeta(2*s-2)/zeta(3*s-2). - Amiram Eldar, Jan 29 2023
a(n) = A034448(A350388(n)). - Amiram Eldar, Sep 09 2023

A247041 Decimal expansion of zeta(5/2).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Sep 10 2014

Zeta(5/2) appears in the expression of the 6th Madelung constant (A247040).

			1.3414872572509171797567696933486121366230376295059865...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

Eric Weisstein's World of Mathematics, Riemann Zeta Function.

Cf. A059750, A078434, A247040.

Mathematica
```
RealDigits[Zeta[5/2], 10, 102] // First
```
PARI
```
zeta(5/2) \\ Michel Marcus, Feb 23 2023
```

A280204 G.f.: Product_{k>=1} (1+x^(k^2)) / (1-x^k).

Original entry on oeis.org

1, 2, 3, 5, 9, 14, 21, 31, 45, 65, 92, 127, 175, 239, 322, 430, 572, 753, 985, 1281, 1657, 2131, 2727, 3471, 4401, 5558, 6988, 8751, 10924, 13588, 16846, 20819, 25653, 31518, 38621, 47195, 57530, 69958, 84869, 102723, 124070, 149532, 179852, 215894, 258668

Offset: 0

Vaclav Kotesovec, Dec 28 2016

nonn

Convolution of A033461 and A000041.

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A000041, A033461, A052335, A078434, A087153, A117144, A264393, A280224, A280225, A369520, A369570.

nmax=50; CoefficientList[Series[Product[(1+x^(k^2))/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

a(n) ~ exp(Pi*sqrt(2*n/3) + 2^(-5/4)*3^(1/4)*(sqrt(2)-1)*Zeta(3/2)*n^(1/4) - 3*(sqrt(2)-1)^2*Zeta(3/2)^2/(64*Pi)) / (2^(5/2)*sqrt(3)*n).

A370256 The number of ways in which n can be expressed as b^2 * c^3, with b and c >= 1.

Original entry on oeis.org

1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0

Offset: 1

Amiram Eldar, Feb 23 2024

First differs from A075802 and A112526 at n = 64.
The least number k such that a(k) = n is A005179(n)^6.
The indices of records are the sixth powers of the highly composite numbers, A002182(n)^6.

			1 = 1^2 * 1^3, so a(1) = 1.
64 = 1^2 * 4^3 = 8^2 * 1^3, so a(64) = 2.
4096 = 64^2 * 1^3 = 8^2 * 4^3 = 1^2 * 16^3, so a(4096)= 3.

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

Cf. A000005, A001694, A002182, A005179, A057523, A075802, A078434, A103221, A112526.

f[p_, e_] := Floor[(e + 2)/2] - Floor[(e + 2)/3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

a(n) = vecprod(apply(x -> (x+2)\2 - (x+2)\3, factor(n)[, 2]));

for(n=1, 100, print1(direuler(p=2, n, 1/((1 - X^2)*(1 - X^3)))[n], ", ")) \\ Vaclav Kotesovec, Feb 23 2024

from math import prod
from sympy import factorint
def A370256(n): return prod((e>>1)+1-(e+2)//3 for e in factorint(n).values()) # Chai Wah Wu, Apr 15 2025

Multiplicative with a(p^e) = A103221(e).
a(n) > 0 if and only if n is a powerful number (A001694).
a(A001694(n)) = A057523(n).
a(n^6) = A000005(n).
Sum_{k=1..n} a(k) ~ zeta(3/2) * sqrt(n) + zeta(2/3) * n^(1/3).
Dirichlet generating function: zeta(2*s)*zeta(3*s). - Vaclav Kotesovec, Feb 23 2024

A261804 Decimal expansion of zeta(7/2).

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, Sep 01 2015

Zeta(7/2) appears in the expression of the 8th Madelung constant (A261805).

			1.126733867317056646427812491854984272221996957403602963842396...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 77.

Eric Weisstein's MathWorld, Riemann Zeta Function
Index entries for constants related to zeta

Cf. A059750, A078434, A247041, A261805.

Mathematica
```
RealDigits[Zeta[7/2], 10, 104] // First
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zeta(7/2) \\ Charles R Greathouse IV, Jun 07 2016

cp's OEIS Frontend

A078470 Continued fraction for zeta(3/2) (A078434).

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A033461 Number of partitions of n into distinct squares.

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A112526 Characteristic function for powerful numbers.

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A059750 Decimal expansion of zeta(1/2) (negated).

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A183097 a(n) = sum of powerful divisors d (including 1) of n.

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A358347 a(n) is the sum of the unitary divisors of n that are squares.

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