Sequences

Nearest integer to Pi^n.

Decimal expansion of square root of Pi.

Decimal expansion of the natural logarithm of 2.

Decimal expansion of square root of 5.

E.g.f.: high-temperature series in J/2kT for logarithm of partition function for the spin-1/2 linear (1D) Heisenberg model.

High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional f.c.c. lattice.

Susceptibility series for f.c.c. lattice.

High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional b.c.c. lattice.

High-temperature series for spin-1/2 Heisenberg susceptibility on b.c.c. lattice.

High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional simple cubic lattice.

High temperature series for spin-1/2 Heisenberg susceptibility on 3-dimensional simple cubic lattice.

Glaisher's chi numbers. a(n) = chi(4*n + 1).

Glaisher's chi numbers chi(p) for p a prime of the form 4m+1.

a(n) = Sum_{d|n, d == 1 mod 4} d^2 - Sum_{d|n, d == 3 mod 4} d^2.

Values taken by reduced totient function psi(n).

Excess of number of divisors of 12n+1 of form 4k+1 over those of form 4k+3.

a(n) = LCM of denominators of Cotesian numbers {C(n,k), 0 <= k <= n}.

Numerators of Cotesian numbers (not in lowest terms): A002176(n)*C(n,0).

Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,1).

Numerators of Cotesian numbers (not in lowest terms): A002176*C(n,2).

Values taken by the half-totient function phi(m)/2.

Least number k such that phi(k) = m, where m runs through the values (A002202) taken by phi.

Highly composite numbers: numbers n where d(n), the number of divisors of n (A000005), increases to a record.

Number of divisors of n-th highly composite number.

a(n) = least primitive factor of 2^(2n+1) - 1.

Smallest primitive factor of 2^(2n+1) + 1.

Sprague-Grundy values for the game of Kayles (octal games .77 and .771).

Sprague-Grundy values for Dawson's Chess (octal game .137).

Sprague-Grundy value for Grundy's game when starting with n tokens.

Pseudo-squares: a(n) = the least nonsquare positive integer which is 1 mod 8 and is a (nonzero) quadratic residue modulo the first n odd primes.

Sum_{n>=0} a(n)*x^n/n!^2 = -log(BesselJ(0,2*sqrt(x))).

Possible values for sum of divisors of n.

Least integer with A000203(a(n)) = A002191(n), where A002191 = range of the sum-of-divisors function A000203.

Decimal expansion of square root of 2.

Decimal expansion of sqrt(3).

Numerators of coefficients for numerical integration.

Denominators of coefficients for numerical integration.

Numerators of coefficients for numerical integration.

Denominators of coefficients for numerical integration.

Least negative primitive root of n-th prime.

Primes of the form 2^q*3^r*5^s + 1.

Superior highly composite numbers: positive integers n for which there is an e > 0 such that d(n)/n^e >= d(k)/k^e for all k > 1, where the function d(n) counts the divisors of n (A000005).

Values taken by totient function phi(m) (A000010).

Companion Pell numbers: a(n) = 2*a(n-1) + a(n-2), a(0) = a(1) = 2.

An ill-conditioned determinant.

The RAND Corporation list of a million random digits.

Numerators of logarithmic numbers (also of Gregory coefficients G(n)).

Denominators of logarithmic numbers (also of Gregory coefficients G(n)).

Numerators of coefficients for numerical integration.

Denominators of coefficients for numerical integration.