A082633 -id:A082633 - cp's OEIS frontend

A000189 Number of solutions to x^3 == 0 (mod n).

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 4, 5, 1, 9, 2, 1, 1, 1, 8, 1, 1, 1, 6, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 4, 7, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 16, 1, 1, 1, 2, 1, 1, 1, 12, 1, 1, 5, 2, 1, 1, 1, 4, 9, 1, 1, 2, 1, 1, 1, 4, 1, 3

Offset: 1

N. J. A. Sloane

Shadow transform of the cubes A000578. - Michel Marcus, Jun 06 2013

			a(4) = 2 because 0^3 == 0, 1^3 == 1, 2^3 == 0, and 3^3 == 3 (mod 4); also, a(9) = 3 because 0^3 = 0, 3^3 == 0, and 6^3 = 0 (mod 9), while x^3 =/= 0 (mod 9) for x = 1, 2, 4, 5, 7, 8. - _Petros Hadjicostas_, Sep 16 2019

T. D. Noe, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.
Steven R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.
Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. (ps, pdf); see Definition 7 for the shadow transform.
Vaclav Kotesovec, Graph - the asymptotic ratio (100000 terms).
OEIS Wiki, Shadow transform.
N. J. A. Sloane, Transforms.

Cf. A000578, A019555.

Array[ Function[ n, Count[ Array[ PowerMod[ #, 3, n ]&, n, 0 ], 0 ] ], 100 ]
f[p_, e_] := p^Floor[2*e/3]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 19 2020 *)

a(n)=my(f=factor(n));prod(i=1,#f[,1],f[i,1]^(2*f[i,2]\3)) \\ Charles R Greathouse IV, Jun 06 2013

for(n=1, 100, print1(direuler(p=2, n, (1 + X + p*X^2)/(1 - p^2*X^3))[n], ", ")) \\ Vaclav Kotesovec, Aug 30 2021

Multiplicative with a(p^e) = p^[2e/3]. - David W. Wilson, Aug 01 2001
a(n) = n/A019555(n). - Petros Hadjicostas, Sep 15 2019
Dirichlet g.f.: zeta(3*s-2) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-1)). - Amiram Eldar, Sep 09 2023
From Vaclav Kotesovec, Sep 09 2023: (Start)
Dirichlet g.f.: zeta(s) * zeta(2*s-1) * zeta(3*s-2) * Product_{p prime} (1 - 1/p^(2*s) - 1/p^(3*s-1) - 1/p^(4*s-2) + 1/p^(4*s-1) + 1/p^(5*s-2)).
Let f(s) = Product_{primes p} (1 - 1/p^(2*s) - 1/p^(3*s-1) - 1/p^(4*s-2) + 1/p^(4*s-1) + 1/p^(5*s-2)).
Sum_{k=1..n} a(k) ~ (f(1)*n/6) * (log(n)^2/2 + (6*gamma - 1 + f'(1)/f(1))*log(n) + 1 - 6*gamma + 11*gamma^2 - 14*sg1 + (6*gamma - 1)*f'(1)/f(1) + f''(1)/(2*f(1))), where
f(1) = Product_{primes p} (1 - 3/p^2 + 2/p^3) = A065473 = 0.2867474284344787341078927127898384464343318440970569956414778593366522431...,
f'(1) = f(1) * Sum_{primes p} 9*log(p) / (p^2 + p - 2) = f(1) * 4.1970213428422788650375569145777616746065054412058004220013841318980729375...,
f''(1) = f'(1)^2/f(1) + f(1) * Sum_{primes p} (-29*p^2 - 17*p + 1) * log(p)^2 / (p^2 + p - 2)^2 = f'(1)^2/f(1) + f(1) * (-21.3646716550082193262514333696570765444176783899223644201265894338042468...),
gamma is the Euler-Mascheroni constant A001620 and sg1 is the first Stieltjes constant (see A082633). (End)

A061502 a(n) = Sum_{k<=n} tau(k)^2, where tau = number of divisors function A000005.

Original entry on oeis.org

1, 5, 9, 18, 22, 38, 42, 58, 67, 83, 87, 123, 127, 143, 159, 184, 188, 224, 228, 264, 280, 296, 300, 364, 373, 389, 405, 441, 445, 509, 513, 549, 565, 581, 597, 678, 682, 698, 714, 778, 782, 846, 850, 886, 922, 938, 942, 1042, 1051, 1087

Offset: 1

N. J. A. Sloane, Jun 14 2001

nonn

R. Ayoub, An Introduction to the Analytic Theory of Numbers, Amer. Math. Soc., 1963; Chapter II, Problem 56.

N. J. A. Sloane, Table of n, a(n) for n = 1..1024
Adrian Dudek, On the Success of Mishandling Euclid's Lemma, arXiv:1602.03555 [math.HO], 2016. See B(n) p. 2.
Chaohua Jia and Ayyadurai Sankaranarayanan, The mean square of the divisor function, Acta Arithmetica 164 (2014), 181-208.
Michaela Cully-Hugill and Timothy Trudgian, Two explicit divisor sums, arXiv:1911.07369 [math.NT], Nov 19 2019
Vaclav Kotesovec, Graph - The asymptotic ratio (1000000 terms)
Florian Luca and László Tóth, The r-th moment of the divisor function: an elementary approach, Journal of Integer Sequences 20 (2017), Article 17.7.4, 8 pp.
Adolf Piltz, Über das Gesetz, nach welchem die mittlere Darstellbarkeit der natürlichen Zahlen als Produkte einer gegebenen Anzahl Faktoren mit der Grösse der Zahlen wächst, 1881.
Ramanujan's Papers, Some formulas in the analytic theory of numbers, Messenger of Mathematics, XLV, 1916, 81-84, Formula (3).
D. Suryanarayana and R. Rama Chandra Rao, On an Asymptotic Formula of Ramanujan, Mathematica Scandinavica, 32, 258-264, 1973.
B. M. Wilson, Proofs of some formulas enunciated by Ramanujan, Proc. London Math. Soc. (2) 21 (1922) 235-255.

Cf. A000005, A035116, A061503, A318755.
Cf. A092742 (A), A245074 (B), A319090 (C), A319091 (D).
Cf. A057434, A072379, A074789.

[&+[NumberOfDivisors(k^2)*Floor(n/k): k in [1..n]]: n in [1..60]]; // Vincenzo Librandi, Sep 10 2016

Table[Sum[DivisorSigma[0, k^2]*Floor[n/k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Aug 30 2018 *)
Accumulate[Table[DivisorSigma[0, n]^2, {n, 1, 50}]] (* Vaclav Kotesovec, Sep 10 2018 *)

for (n=1, 1024, write("b061502.txt", n, " ", sum(k=1, n, numdiv(k)^2)) ) \\ Harry J. Smith, Jul 23 2009

vector(60, n, sum(k=1, n, numdiv(k)^2)) \\ Michel Marcus, Jul 23 2015

first(n)=my(v=vector(n),s); forfactored(k=1,n, v[k[1]] = s += numdiv(k)^2); v; \\ Charles R Greathouse IV, Nov 28 2018

a(n) = Sum_{k=1..n} tau(k^2)*floor(n/k).
Asymptotic to A*n*log(n)^3 + B*n*log(n)^2 + C*n*log(n) + D*n + O(n^(1/2+eps)) where A = 1/Pi^2 and B = (12*gamma-3)/Pi^2 - 36*zeta'(2)/Pi^4. [corrected by Vaclav Kotesovec, Aug 30 2018]
C = 36*gamma^2/Pi^2 - (288*z1/Pi^4 + 24/Pi^2)*gamma + (864*z1^2/Pi^6 + 72*z1/Pi^4 - 72/Pi^4*z2 + 6/Pi^2) - 24*g1/Pi^2 and D = 24*gamma^3/Pi^2 - (432*z1 /Pi^4+ 36/Pi^2)*gamma^2 + (3456*z1^2/Pi^6 + 288*(z1-z2)/Pi^4 + 24/Pi^2 - 72*g1/Pi^2)*gamma + g1*(288*z1/Pi^4 + 24/Pi^2)-10368*z1^3/Pi^8 - 864*z1^2/Pi^6 + 1728*z2*z1/Pi^6 + 72*(z2-z1)/Pi^4- 48*z3/Pi^4 + (12*g2-6)/Pi^2, where gamma is the Euler-Mascheroni constant A001620, z1 = Zeta'(2) = A073002, z2 = Zeta''(2) = A201994, z3 = Zeta'''(2) = A201995 and g1, g2 are the Stieltjes constants, see A082633 and A086279. - Vaclav Kotesovec, Sep 10 2018
See Cully-Hugill & Trudgian, Theorem 2, for an explicit version of the asymptotic given above. - Charles R Greathouse IV, Nov 19 2019

Definition corrected by N. J. A. Sloane, May 25 2008

A055155 a(n) = Sum_{d|n} gcd(d, n/d).

Original entry on oeis.org

1, 2, 2, 4, 2, 4, 2, 6, 5, 4, 2, 8, 2, 4, 4, 10, 2, 10, 2, 8, 4, 4, 2, 12, 7, 4, 8, 8, 2, 8, 2, 14, 4, 4, 4, 20, 2, 4, 4, 12, 2, 8, 2, 8, 10, 4, 2, 20, 9, 14, 4, 8, 2, 16, 4, 12, 4, 4, 2, 16, 2, 4, 10, 22, 4, 8, 2, 8, 4, 8, 2, 30, 2, 4, 14, 8, 4, 8, 2, 20, 17, 4, 2, 16, 4, 4, 4, 12, 2, 20, 4, 8, 4, 4

Offset: 1

Leroy Quet, Jul 02 2000

a(n) is odd iff n is odd square. - Vladeta Jovovic, Aug 27 2002
From Robert Israel, Dec 26 2015: (Start)
a(n) >= A000005(n), with equality iff n is squarefree (i.e., is in A005117).
a(n) = 2 iff n is prime. (End)

			a(9) = gcd(1,9) + gcd(3,3) + gcd(9,1) = 5, since 1, 3, 9 are the positive divisors of 9.

Robert Israel, Table of n, a(n) for n = 1..10000
Ekkehard Krätzel, Werner Nowak and László Tóth, On certain arithmetic functions involving the greatest common divisor, Cent. Eur. J. Math., Vol. 10, No. 2 (2012), pp. 761-774.
Manfred Kühleitner and Werner Georg Nowak, On a question of A. Schinzel: Omega estimates for a special type of arithmetic functions, Central European Journal of Mathematics, Vol. 11, No. 3 (2013), pp. 477-486, preprint, arXiv: 1204.1146 [math.NT], 2012.
Project Euler, Problem 530 - GCD of Divisors.
László Tóth, Multiplicative arithmetic functions of several variables: a survey, in: T. Rassias and P. Pardalos (eds.), Mathematics Without Boundaries, Springer, New York, N.Y., 2014, pp. 483-514, arXiv preprint, arXiv:1310.7053 [math.NT], 2013-2014.

Cf. A000005, A000188, A001620, A005117, A057670, A073002. A082633, A201994.

Cf. A000010.

N:= 1000: # to get a(1) to a(N)
V:= Vector(N):
for k from 1 to N do
   for j from 1 to floor(N/k) do
     V[k*j]:= V[k*j]+igcd(k,j)
   od
od:
convert(V,list); # Robert Israel, Dec 26 2015

Table[DivisorSum[n, GCD[#, n/#] &], {n, 94}] (* Michael De Vlieger, Sep 23 2017 *)
f[p_, e_] := If[EvenQ[e], (p^(e/2)*(p+1)-2)/(p-1), 2*(p^((e+1)/2)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 30 2020 *)

a(n) = sumdiv(n, d, gcd(d, n/d)); \\ Michel Marcus, Aug 03 2016

from sympy import divisors, gcd
def A055155(n): return sum(gcd(d,n//d) for d in divisors(n,generator=True)) # Chai Wah Wu, Aug 19 2021

Multiplicative with a(p^e) = (p^(e/2)*(p+1)-2)/(p-1) for even e and a(p^e) = 2*(p^((e+1)/2)-1)/(p-1) for odd e. - Vladeta Jovovic, Nov 01 2001
Dirichlet g.f.: (zeta(s))^2*zeta(2s-1)/zeta(2s); inverse Mobius transform of A000188. - R. J. Mathar, Feb 16 2011
Dirichlet convolution of A069290 and A008966. - R. J. Mathar, Oct 31 2011
Sum_{k=1..n} a(k) ~ 3*n / (2*Pi^6) * (Pi^4 * log(n)^2 + ((8*g - 2)*Pi^4 - 24 * Pi^2 * z1) * log(n) + 2*Pi^4 * (1 - 4*g + 5*g^2 - 6*sg1) + 288 * z1^2 - 24 * Pi^2 * (-z1 + 4*g*z1 + 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 01 2019
a(n) = (1/n)*Sum_{i=1..n} sigma(gcd(n,i^2)). - Ridouane Oudra, Dec 30 2020
a(n) = Sum_{k=1..n} gcd(gcd(n,k),n/gcd(n,k))/phi(n/gcd(n,k)), where phi = A000010. - Richard L. Ollerton, May 09 2021

A086281 Decimal expansion of 4th Stieltjes constant gamma_4.

Original entry on oeis.org

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

Offset: 0

Eric W. Weisstein, Jul 14 2003

			0.0023253...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 166.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint, arXiv:2210.04609 [math.NT], 2022.
Eric Weisstein's World of Mathematics, Stieltjes Constants
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279, A086280, A086282, A183141, A183167, A183206, A184853, A184854.

Join[{0, 0}, RealDigits[ N[ -StieltjesGamma[4], 103]][[1]]] (* Jean-François Alcover, Nov 07 2012 *)

Using the abbreviations a = log(z^2 + 1/4)/2, b = arctan(2*z) and c = cosh(Pi*z) then gamma_4 = -(Pi/5)*Integral_{0..infinity} (a^5-10*a^3*b^2+5*a*b^4)/c^2. The general case is for n>=0 (which includes Euler's gamma as gamma_0) gamma_n = (-Pi/ (n+1))*Integral_{0..infinity} sigma(n+1)/c^2, where sigma(n) = Sum_{k=0.. floor(n/2)}(-1)^k*binomial(n,2*k)*b^(2*k)*a^(n-2*k). - Peter Luschny, Apr 19 2018

A086282 Decimal expansion of 5th Stieltjes constant gamma_5.

Original entry on oeis.org

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

Offset: 0

Eric W. Weisstein, Jul 14 2003

			0.00079332381730106270175333487744444483...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 166.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint, arXiv:2210.04609 [math.NT], 2022.
Eric Weisstein's World of Mathematics, Stieltjes Constants
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279, A086280, A086281, A183141, A183167, A183206, A184853, A184854.

evalf(gamma(5)); # R. J. Mathar, Feb 02 2011

Join[{0, 0, 0}, RealDigits[ N[ -StieltjesGamma[5], 102]][[1]]]  (* Jean-François Alcover, Nov 07 2012 *)

A183141 Decimal expansion of 6th Stieltjes constant, negated.

Original entry on oeis.org

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

Offset: 0

Paul Muljadi, Feb 01 2011

			-0.000238769345430199609872421841908004277783715156358....

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint (2022). arXiv:2210.04609 [math.NT]
Eric Weisstein's World of Mathematics, Stieltjes Constants
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279, A086280, A086281, A086282, A183167, A183206, A184853, A184854.

evalf(gamma(6)); # R. J. Mathar, Feb 02 2011

RealDigits[StieltjesGamma[6], 10, 100][[1]]

A183167 Decimal expansion of 7th Stieltjes constant, negated.

Original entry on oeis.org

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

Offset: 0

Paul Muljadi, Feb 01 2011

			-0.000527289567057751046074097505478858281996253472969895...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint (2022). arXiv:2210.04609 [math.NT]
Eric Weisstein's World of Mathematics, Stieltjes Constants
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279, A086280, A086281, A086282, A183141, A183206, A184853, A184854.

evalf(gamma(7)) ; # R. J. Mathar, Feb 02 2011

Join[{0, 0, 0}, RealDigits[StieltjesGamma[7], 10, 100][[1]]] (* Alonso del Arte, Feb 01 2011 *)

A183206 Decimal expansion of 8th Stieltjes constant, negated.

Original entry on oeis.org

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

Offset: 0

Paul Muljadi, Feb 01 2011

			-0.00035212335380303950960205216500120874172918053379235....

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint (2022). arXiv:2210.04609 [math.NT]
Eric Weisstein's World of Mathematics, Stieltjes Constants
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279-A086282, A183141, A183167, A184853, A184854.

Maple
```
evalf(gamma(8)) ;
```

RealDigits[StieltjesGamma[8], 10, 100][[1]] (* Alonso del Arte, Feb 01 2011 *)

A184853 Decimal expansion of 9th Stieltjes constant, negated.

Original entry on oeis.org

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

Offset: 0

Paul Muljadi, Feb 01 2011

			-0.000034394774418088048177914623798227390620789538594442....

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint (2022). arXiv:2210.04609 [math.NT]
Eric Weisstein's World of Mathematics, Stieltjes Constants
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279, A086280, A086281, A086282, A183141, A183167, A183206, A184854.

evalf(gamma(9)); # R. J. Mathar, Feb 02 2011

Join[{0, 0, 0, 0}, RealDigits[ N[ -StieltjesGamma[9], 101]][[1]]] (* Jean-François Alcover, Nov 07 2012 *)

A184854 Decimal expansion of 10th Stieltjes constant.

Original entry on oeis.org

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

Offset: 0

Paul Muljadi, Feb 01 2011

			0.00020533281490906479468372228923706530295985377416676....

Steven R. Finch, "Stieltjes Constants." Section 2.21 in Mathematical Constants. Cambridge: Cambridge University Press (2003), 166 - 171.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Krzysztof Maślanka and Andrzej Koleżyński, The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm, arXiv preprint arXiv:2210.04609 [math.NT], 2022.
Eric Weisstein, Stieltjes Constants from Mathworld
Wikipedia, Stieltjes constants

Cf. A001620, A082633, A086279, A086280, A086281, A086282, A183141, A183167, A183206, A184853

RealDigits[StieltjesGamma[10], 10, 100][[1]] (* Alonso del Arte, Feb 01 2011 *)

cp's OEIS Frontend

A000189 Number of solutions to x^3 == 0 (mod n).

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A061502 a(n) = Sum_{k<=n} tau(k)^2, where tau = number of divisors function A000005.

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A055155 a(n) = Sum_{d|n} gcd(d, n/d).

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A086281 Decimal expansion of 4th Stieltjes constant gamma_4.

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A086282 Decimal expansion of 5th Stieltjes constant gamma_5.

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A183141 Decimal expansion of 6th Stieltjes constant, negated.

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A183167 Decimal expansion of 7th Stieltjes constant, negated.

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