Sequences

Smallest square containing exactly n 4's.

Smallest square containing exactly n 5's.

Smallest square containing exactly n 6's.

Smallest square containing exactly n 7's.

Smallest square containing exactly n 8's.

Smallest square containing exactly n 9's.

Smallest triangular number containing exactly n 0's.

Smallest triangular number containing exactly n 1's.

Smallest triangular number containing exactly n 2's.

Smallest triangular number containing exactly n 3's.

Smallest triangular number containing exactly n 4's.

Smallest triangular number containing exactly n 5's.

Smallest triangular number containing exactly n 6's.

Smallest triangular number containing exactly n 7's.

Smallest triangular number containing exactly n 8's.

Smallest triangular number containing exactly n 9's.

Smallest cube containing exactly n 0's.

Smallest cube containing exactly n 1's.

Smallest cube containing exactly n 2's.

Smallest cube containing exactly n 3's.

Smallest cube containing exactly n 4's.

Smallest cube containing exactly n 5's.

Smallest cube containing exactly n 6's.

Smallest cube containing exactly n 7's.

Smallest cube containing exactly n 8's.

Smallest cube containing exactly n 9's.

Numbers whose number of divisors is a power of 2.

Number of integers m <= 2^n such that d(m) = 2^k for some k = 0, 1, 2, 3, ...

a(n) is the number of numbers k with 2^(n-1) < k <= 2^n having a number of divisors that is a power of 2.

Numbers k such that d(i) is a power of 2 for all k <= i <= k+6, where d(i) = number of divisors of i.

Deficit of central binomial coefficients in terms of number of prime factors: a(n) shows how many fewer prime factors the n-th central binomial coefficient has than n!.

a(n) = T(n,n), array T given by A047858.

a(n) = T(3,n), array T given by A048471.

a(n) = (2*(1 + n + (((10^n-1)/9) - n)/9)).

a(n) = T(4,n), array T given by A048471.

a(n) = T(5,n), array T given by A048471.

a(n) = T(6,n), array T given by A048471.

a(n) = T(7,n), array T given by A048471.

a(n) = T(8,n), array T given by A048471.

a(n) = T(0,n) + T(1,n-1) + ... + T(n,0), array T given by A048471.

a(n) = 2^(n-1)*(3^n-1) + 1.

List of pairs (m,2m) where m is the least unused positive number.

a(n) = phi(prime(n)) - prime(phi(n)).

Numbers whose binary representation ends in an odd number of zeros.

Hamming weight of 3n: number of 1's in binary expansion of 3n.

Integers which when multiplied by 3 have an odd number of 1's in their binary expansion (cf. A000069).

Number of multiples of 3 in 0..2^n-1 with an even sum of base-2 digits.

Squared distances that can arise in any Barlow packing of spheres of diameter sqrt(3) (the scale being the simplest one that makes this an integer sequence).

Squared distances that cannot arise in any Barlow packing of spheres of diameter sqrt(3) (the scale being the simplest one that makes this an integer sequence).

StirlingS2[ n,m ] triangle summed down the columns.