A073002 -id:A073002 - cp's OEIS frontend

A261506 Decimal expansion of -zeta'(4).

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

Offset: 0

Vaclav Kotesovec, Aug 22 2015

			0.06891126589612537984882936558744082715001637487137...

J. B. Rosser, L. Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. J. Math. 6 (1) (1962) 64-94, Table IV

Cf. A075700 (0), A073002 (2), A244115 (3).

Cf. A084448 (-1), A240966 (-2), A259068 (-3), A259069 (-4), A259070 (-5), A259071 (-6), A259072 (-7), A259073 (-8).

Flatten[{0, RealDigits[-Zeta'[4], 10, 105][[1]]}]

Sum_{n>=1} log(n) / n^4.

A034761 Dirichlet convolution of sigma(n) with itself.

Original entry on oeis.org

1, 6, 8, 23, 12, 48, 16, 72, 42, 72, 24, 184, 28, 96, 96, 201, 36, 252, 40, 276, 128, 144, 48, 576, 98, 168, 184, 368, 60, 576, 64, 522, 192, 216, 192, 966, 76, 240, 224, 864, 84, 768, 88, 552, 504, 288, 96, 1608, 178, 588, 288, 644, 108, 1104, 288, 1152, 320, 360

Offset: 1

Erich Friedman

T. D. Noe, Table of n, a(n) for n=1..10000

Cf. A000005, A000203 (sigma), A001620, A073002, A074962, A134577.

f[p_, e_] := ((e + 1)*p^(e + 3) - (e + 3)*(p^(e + 2) - p + 1) + 2)/(p - 1)^3; f[2, e_] := (e - 1)*2^(e + 2) + e + 5; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] (* Amiram Eldar, Oct 16 2022 *)

Dirichlet g.f.: zeta^2(s)*zeta^2(s-1).
Multiplicative with a(2^e) = (e-1) 2^(e+2) + e + 5, a(p^e) = ((1+e)p^(e+3) - (3+e)(p^(e+2)-p+1) + 2)/(p-1)^3, p > 2. - Mitch Harris, Jun 27 2005 [corrected by Amiram Eldar, Oct 16 2022 and Sep 12 2023]
Equals A134577 * A000005. - Gary W. Adamson, Nov 02 2007
Also the Dirichlet convolution A000005 by A038040. - R. J. Mathar, Apr 01 2011
Sum_{k=1..n} a(k) ~ Pi^2 * n^2 * (2*Pi^2 * log(n) + (4*gamma - 1)*Pi^2 + 24*zeta'(2)) / 144, where gamma is the Euler-Mascheroni constant A001620 and Zeta'(2) = A073002. Equivalently, Sum_{k=1..n} a(k) ~ Pi^4 * n^2 * (2*log(n) - 1 + 8*gamma - 48*log(A) + 4*log(2*Pi)) / 144, where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jan 28 2019

A201995 Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Dec 07 2011

			zeta'''(2) = -6.00014580284304486564394121753784..

Jason Bard, Table of n, a(n) for n = 1..2000
B. K. Choudhury, The Riemann zeta-function and its derivatives, Proc. R. Soc. Lond A 445 (1995) 477-499.
Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21.

Cf. A013661, A073002, A201994.

Maple
```
evalf(Zeta(3,2));
```

RealDigits[ Zeta'''[2], 10, 93] // First (* Jean-François Alcover, Feb 20 2013 *)

zeta'''(2)= -Sum_{k>=1} log^3(k)/k^2.

Equals 3! + Sum_{k>=0} (-1)^k*gamma(3+k)/k!, where gamma(.) are the Stieltjes constants A001620, A082633, A086279 etc. [Choudhury, Thm. 4]

A295295 Sum of squarefree divisors of the powerful part of n: a(n) = A048250(A057521(n)).

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 6, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 12, 1, 1, 1, 3, 1, 1, 1, 3, 4, 1, 1, 3, 8, 6, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 3, 1, 1, 1, 12, 1, 1, 6, 3, 1, 1, 1, 3, 4, 1, 1, 3, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 8, 4, 18, 1, 1, 1, 3, 1

Offset: 1

Antti Karttunen, Nov 25 2017

The sum of the squarefree divisors of n whose square divides n. - Amiram Eldar, Oct 13 2023

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to sums of divisors.

Cf. A000203, A003557, A048250, A057521, A064549, A092261, A295294, A344137.

Cf. A001620, A013661, A073002.

Array[DivisorSum[#/Denominator[#/Apply[Times, FactorInteger[#][[All, 1]]]^2], # &, SquareFreeQ] &, 105] (* Michael De Vlieger, Nov 26 2017, after Jean-François Alcover at A057521 *)
f[p_, e_] := If[e == 1, 1, p+1] ; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 18 2023 *)

a(n) = my(f=factor(n)); for (i=1, #f~, if (f[i,2]==1, f[i,1]=1)); sumdiv(factorback(f), d, d*issquarefree(d)); \\ Michel Marcus, Jan 29 2021

Multiplicative with a(p) = 1 and a(p^e) = (p+1) for e > 1.
a(n) = A048250(A057521(n)) = A048250(A064549(A003557(n))).
a(n) = A048250(n) / A092261(n).
a(n) = Sum_{d^2|n} d * mu(d)^2. - Wesley Ivan Hurt, Feb 13 2022
From Amiram Eldar, Sep 18 2023: (Start)
Dirichlet g.f.: zeta(s) * zeta(2*s-1) / zeta(4*s-2).
Sum_{k=1..n} a(k) ~ (3*n/Pi^2) * (log(n) + 3*gamma - 1 - 4*zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). (End)
a(n) = A048250(n) - A344137(n). - Amiram Eldar, Oct 13 2023

A061503 a(n) = Sum_{k=1..n} tau(k^2), where tau is the number of divisors function A000005.

Original entry on oeis.org

1, 4, 7, 12, 15, 24, 27, 34, 39, 48, 51, 66, 69, 78, 87, 96, 99, 114, 117, 132, 141, 150, 153, 174, 179, 188, 195, 210, 213, 240, 243, 254, 263, 272, 281, 306, 309, 318, 327, 348, 351, 378, 381, 396, 411, 420, 423, 450, 455, 470, 479, 494, 497

Offset: 1

N. J. A. Sloane, Jun 14 2001

nonn

a(n) is the number of pairs of positive integers <= n with their LCM <= n. - Andrew Howroyd, Sep 01 2019

Mentioned by Steven Finch in a posting to the Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Jun 13 2001.

Harry J. Smith, Table of n, a(n) for n = 1..1024
Kevin A. Broughan, Restricted divisor sums, Acta Arithmetica, vol. 101, (2002), pp. 105-114.
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 19.
Vaclav Kotesovec, Graph - the asymptotic ratio
Eric Weisstein's World of Mathematics, Stieltjes Constants

Cf. A000005, A061502. Partial sums of A048691.

List([1..60],n->Sum([1..n],k->Tau(k^2))); # Muniru A Asiru, Mar 09 2019

with(numtheory): a:=n->add(tau(k^2),k=1..n): seq(a(n),n=1..60); # Muniru A Asiru, Mar 09 2019

DivisorSigma[0, Range[60]^2] // Accumulate (* Jean-François Alcover, Nov 25 2013 *)

for (n=1, 1024, write("b061503.txt", n, " ", sum(k=1, n, numdiv(k^2)))) \\ Harry J. Smith, Jul 23 2009

t=0;v=vector(60,n,t+=numdiv(n^2)) \\ Charles R Greathouse IV, Nov 08 2012

from math import prod
from sympy import factorint
def A061503(n): return sum(prod(2*e+1 for e in factorint(k).values()) for k in range(1,n+1)) # Chai Wah Wu, May 10 2022

def A061503(n) :
    tau = sloane.A000005
    return add(tau(k^2) for k in (1..n))
[ A061503(i) for i in (1..19)] # Peter Luschny, Sep 15 2012

a(n) = Sum_{j=1..n^2} floor(n/A019554(j)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jul 20 2002
a(n) = Sum_{i=1..n} 2^omega(i) * floor(n/i). - Enrique Pérez Herrero, Sep 15 2012
a(n) ~ 3/Pi^2 * n log^2 n. - Charles R Greathouse IV, Nov 08 2012
a(n) ~ 3*n/Pi^2 * (log(n)^2 + log(n)*(-2 + 6*g - 24*z/Pi^2) + 2 - 6*g + 6*g^2 - 6*sg1 + 288*z^2/Pi^4 - 24*(-z + 3*g*z + z2)/ Pi^2), where g is the Euler-Mascheroni constant A001620, sg1 is the first Stieltjes constant (see A082633), z = Zeta'(2) (see A073002), z2 = Zeta''(2) = A201994. - Vaclav Kotesovec, Jan 30 2019
a(n) = Sum_{k=1..n} A064608(floor(n/k)). - Daniel Suteu, Mar 09 2019

Name corrected by Peter Luschny, Sep 15 2012

A078644 a(n) = tau(2*n^2)/2.

Original entry on oeis.org

1, 2, 3, 3, 3, 6, 3, 4, 5, 6, 3, 9, 3, 6, 9, 5, 3, 10, 3, 9, 9, 6, 3, 12, 5, 6, 7, 9, 3, 18, 3, 6, 9, 6, 9, 15, 3, 6, 9, 12, 3, 18, 3, 9, 15, 6, 3, 15, 5, 10, 9, 9, 3, 14, 9, 12, 9, 6, 3, 27, 3, 6, 15, 7, 9, 18, 3, 9, 9, 18, 3, 20, 3, 6, 15, 9, 9, 18, 3, 15, 9, 6, 3, 27, 9, 6, 9, 12, 3, 30, 9, 9, 9, 6, 9

Offset: 1

Vladeta Jovovic, Dec 13 2002

Inverse Moebius transform of A068068. Number of elements in the set {(x,y): x is odd, x|n, y|n, gcd(x,y)=1}.
The number of Pythagorean points (x,y), 0 < x < y, located on the hyperbola y = 2n(x-n)/(x-2n) and having "excess" x+y-z = 2n. - Seppo Mustonen, Jun 07 2005
a(n) is the number of Pythagorean triangles with radius of the inscribed circle equal to n. For number of primitive Pythagorean triangles having inradius n, see A068068(n). - Ant King, Mar 06 2006
Dirichlet convolution of A048691 and A154269. - R. J. Mathar, Jun 01 2011
Number of distinct L-shapes of thickness n where the L area equals the rectangular area that it "contains". Visually can be thought as those areas of A156688 (surrounded by equal border of thickness n: 2xy = (x+2n)(y+2n), x and y positive integers) where both x and y are even, so they can be split into L-shapes. So L-shapes have formula: 2xy = (x+n)(y+n). - Juhani Heino, Jul 23 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
S. Mustonen, Visualization and characterization of Pythagorean triples
Seppo Mustonen, Visualization and characterization of Pythagorean triples [Local copy]
T. Omland, How many Pythagorean triples with given inradius?, J. Numb. Theory 170 (2017) 1-2.

Cf. A000005, A001105, A048691.

[NumberOfDivisors(2*n^2)/2 : n in [1..100]]; // Vincenzo Librandi, Aug 14 2018

with(numtheory): seq(add(mobius(2*d)^2*tau(n/d), d in divisors(n)), n=1..100); # Ridouane Oudra, Nov 17 2019

Table[DivisorSigma[0, 2 n^2] / 2, {n, 100}] (* Vincenzo Librandi, Aug 14 2018 *)

a(n) = numdiv(2*n^2)/2; \\ Michel Marcus, Oct 04 2013

[sigma(2*n^2,0)/2 for n in range(1,100)] # Joerg Arndt, May 12 2014

Multiplicative with a(2^e) = e+1, a(p^e) = 2*e+1, p > 2. a(n) = tau(n^2) if n is odd, a(n) = tau(n^2) - a(n/2) if n is even.
Dirichlet g.f.: zeta^3(s)/(zeta(2s)*(1+1/2^s)). - R. J. Mathar, Jun 01 2011
Sum_{k=1..n} a(k) ~ 2*n / (9*Pi^2) * (9*log(n)^2 + 6*log(n) * (-3 + 9*g + log(2) - 36*Pi^(-2)*z1) + 18 + 54*g^2 + 18*g * (log(2) - 3) - 6*log(2) - log(2)^2 - 54*sg1 + 2592*z1^2/Pi^4 - 72*Pi^-2*(9*g*z1 + (log(2) - 3)*z1 + 3*z2)), where g is the Euler-Mascheroni constant A001620, sg1 is the first Stieltjes constant A082633, z1 = Zeta'(2) = A073002, z2 = Zeta''(2) = A201994. - Vaclav Kotesovec, Feb 02 2019
a(n) = Sum_{d|n} mu(2d)^2*tau(n/d), Dirichlet convolution of A323239 and A000005. - Ridouane Oudra, Nov 17 2019
a(n) = A361689(n)/2. - R. J. Mathar, Mar 21 2023

A225746 Decimal expansion of the logarithm of Glaisher's constant.

Original entry on oeis.org

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

Offset: 1

Jean-François Alcover, May 14 2013

			0.248754477033784262547252993576113976097369713668535116999855639690693032999...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin constant, p. 135.

Jesús Guillera and Jonathan Sondow, Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent, The Ramanujan Journal, Vol. 16, No. 3 (2008), pp. 247-270; arXiv preprint, arXiv:math/0506319 [math.NT], 2005-2006.
Jean-Christophe Pain, Two integral representations for the logarithm of the Glaisher-Kinkelin constant, arXiv:2405.05264 [math.GM], 2024.
Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant.

Cf. A001620, A073002, A074962, A084448.

RealDigits[Log[Glaisher], 10, 100] // First

1/12-zeta'(-1) \\ Charles R Greathouse IV, Dec 12 2013

Equals 1/12 - zeta'(-1).
Also equals (gamma + log(2*Pi))/12 -zeta'(2)/(2*Pi^2).
From Amiram Eldar, Apr 15 2021: (Start)
Equals lim_{n->oo} (Sum_{k=1..n} k*log(k) - (n^2/2 + n/2 + 1/12)*log(n) + n^2/4).
Equals 1/8 + (1/2) * Sum_{n>=0} ((1/(n+1)) * Sum_{k=0..n} (-1)^(k+1) * binomial(n,k) * (k+1)^2 * log(k+1)) (Guillera and Sondow, 2008). (End)

A358040 a(n) is the number of divisors of the n-th cubefree number.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 3, 4, 2, 6, 2, 4, 4, 2, 6, 2, 6, 4, 4, 2, 3, 4, 6, 2, 8, 2, 4, 4, 4, 9, 2, 4, 4, 2, 8, 2, 6, 6, 4, 2, 3, 6, 4, 6, 2, 4, 4, 4, 2, 12, 2, 4, 6, 4, 8, 2, 6, 4, 8, 2, 2, 4, 6, 6, 4, 8, 2, 4, 2, 12, 4, 4, 4, 2, 12, 4, 6, 4, 4, 4, 2, 6, 6, 9, 2

Offset: 1

Amiram Eldar, Oct 29 2022

nonn

The analogous sequence with squarefree numbers is A072048.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Zhu Weiyi, On the cube free number sequences, Smarandache Notions J., Vol. 14 (2004), pp. 199-202.

Cf. A000005, A001620 (gamma), A004709, A072048, A073002 (-zeta'(2)), A147533 (2*gamma-1), A358039.

DivisorSigma[0, Select[Range[100], Max[FactorInteger[#][[;;, 2]]] < 3 &]]

from sympy import mobius, integer_nthroot, divisor_count
def A358040(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**3) for k in range(1, integer_nthroot(x,3)[0]+1))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return divisor_count(m) # Chai Wah Wu, Aug 06 2024

a(n) = A000005(A004709(n)).

Sum_{k=1..n} a(k) = (36*c_1/Pi^4) * n * (log(n) + (2*gamma - 1) - 24*zeta'(2)/Pi^2 - 4*c_2) + O(n^(1/2 + eps)), where c_1 = Product_{p prime} ((p^2+2*p+3)/(p+1)^2) = 1.58095136661854869148023... and c_2 = Sum_{p prime} p*log(p)/((p+1)*(p^2+2*p+3)) = 0.229224... (Weiyi, 2004).

A161166 Decimal expansion of a constant in the linear term in the growth rate of unitary squarefree divisors.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Jun 04 2009

Other constituents of the linear term are in A065463, A073002, A001620 and A059956.

			0.748372333429674...

D. Suryanarayana and V. Siva Rama Prasad, The number of k-ary, k+1-free divisors of an integer, J. Reine Angew. Math. 276 (1975) 15-35.

Steven R. Finch, Unitarism and Infinitarism, February 25, 2004. [Cached copy, with permission of the author]
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 50.

ratfun = (2*p + 1)/((p + 1)*(p^2 + p - 1)); zetas = 0; ratab = Table[konfun = Simplify[ratfun + c/(p^power - 1)] // Together; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*Zeta'[power]/Zeta[power] /. sol; ratfun = konfun /. sol, {power, 2, 25}]; Do[Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 120]], {m, 2000, 20000, 2000}] (* Vaclav Kotesovec, Jun 24 2020 *)

Equals sum_{primes p} (2p+1)*log(p)/((p+1)(p^2+p-1)) = sum_p log(p)*[2/(p^2-1)-3/p^3-1)+4/(p^4-1)-10/(p^5-1)....] where the terms accumulate; this is essentially the logarithmic derivative of the Riemann zeta function at s=2, 3, 4,...

More digits from Vaclav Kotesovec, Jun 24 2020

A210593 Decimal expansion of the series limit of Sum_{k>=1} (-1)^k*log(k)/k^2.

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Mar 23 2012

First derivative of the Dirichlet eta-function eta(s) at s=2.

Phatisena et al. misspell "Euler" and provide the wrong sign and an invalid 7th digit.

			0.101316578163504501886002882212242183659384776374911163334294247196204...

G. C. Greubel, Table of n, a(n) for n = 0..10000
S. Phatisena, R. E. Amritkar, P. V. Panat, Exchange and correlation potential for a two-dimensional electron gas at finite temperatures, Phys. Rev. A 34 (1986) 5070.
Wikipedia, Dirichlet eta function

Cf. A073002, A013661, A002162, A091812 (s=1), A375506 (s=3/2), A349220 (s=3), A349252 (s=4).

1/2*log(2)*Zeta(2)+Zeta(1,2)/2 ; evalf(%) ;

N[(1/12)*Pi^2*(Log[4] - 12*Log[Glaisher] + Log[Pi] + EulerGamma), 105] // RealDigits // First (* Jean-François Alcover, Feb 05 2013 *)

(log(2)*zeta(2)+zeta'(2))/2 \\ Charles R Greathouse IV, Mar 28 2012

Decimal expansion of (log(2)*zeta(2) + zeta'(2)) / 2.

Extended to 105 digits by Jean-François Alcover, Feb 05 2013

cp's OEIS Frontend

A261506 Decimal expansion of -zeta'(4).

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A034761 Dirichlet convolution of sigma(n) with itself.

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A201995 Decimal expansion of the absolute value of zeta'''(2), the third derivative of the Riemann zeta function at 2.

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A295295 Sum of squarefree divisors of the powerful part of n: a(n) = A048250(A057521(n)).

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A061503 a(n) = Sum_{k=1..n} tau(k^2), where tau is the number of divisors function A000005.

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A078644 a(n) = tau(2*n^2)/2.

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A225746 Decimal expansion of the logarithm of Glaisher's constant.

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