Sequences

a(n) = 24^(5*n + 2).

a(n) = 24^(5*n + 3).

a(n) = 24^(5*n + 4).

Number of distinct nonzero absolute values of Sum_{j=1..n} sigma_j * exp(i * Pi * j / n) where sigma_j = +- 1.

a(n) = F(n) + L(n) + n, where F(n) (A000045) and L(n) (A000204) are Fibonacci and Lucas numbers respectively.

Numbers k such that the sum of the first k primes is prime.

a(n) is prime and sum of all primes <= a(n) is prime.

Primes equal to the sum of the first k primes for some k.

Numbers n such that sum of first n composites is composite.

Composite numbers k such that the sum of all composites <= k is composite.

Composite numbers that are equal to the sum of the first k composites for some k.

Number of labeled connected graphs with n nodes and 0 cutpoints (blocks or nonseparable graphs).

Number of labeled connected graphs with n vertices and 1 cutpoint.

Number of labeled connected graphs with n nodes and 2 cutpoints.

Number of labeled connected graphs with n nodes and 3 cutpoints.

a(n) = (2*n)! * D_{2*n}, where D_{2*n} = (1/Pi) * Integral_{x=0..oo} [1 - x^(2*n) / Product_{j=1..n} (x^2+j^2)] dx.

Begin with 2n cards in n piles of 2, the piles being {1,1},{2,2},{3,3},...,{n,n}. How many transpositions of adjacent (single) cards are needed to reverse the order of the piles?

Number of (positive) squarefree numbers < n.

Numbers that are not squarefree. Numbers that are divisible by a square greater than 1. The complement of A005117.

Sum of first a(n) squarefrees is squarefree.

a(n) is squarefree and sum of all squarefrees <= a(n) is squarefree.

Integers that are squarefree and also the sum of first k squarefrees for some k.

Numbers k such that the sum of the first k nonsquarefree numbers is nonsquarefree.

Nonsquarefree numbers k such that the sum of all nonsquarefree numbers <= k is nonsquarefree.

a(n) is nonsquarefree and is sum of first k nonsquarefrees for some k.

a(n) = Sum_{k=1..n} floor(n/k^2).

a(n) = Sum_{k=1..n} floor(n/k^3).

a(n) = Sum_{k=1..n} floor(n/k^4).

Partial sums of sequence A001221 (number of distinct primes dividing n).

a(n) = Sum_{k=1..n} floor(n/prime(k)^2).

a(n) = Sum_{k = 1..n} floor(n/prime(k)^3).

Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows.

Period of continued fraction for sqrt(m), m = n-th nonsquare.

Sum of terms in period of continued fraction for square root of the n-th nonsquare.

Least d such that period of continued fraction for sqrt(d) contains n (n^2+2 if n odd, (n/2)^2+1 if n even).

Least d for which the number with continued fraction [n,n,n,n...] is in Q(sqrt(d)).

Positions of 1's in Kolakoski sequence (A000002).

Positions of 2's in Kolakoski sequence (A000002).

Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2), take limit.

Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); a(n) = length of n-th term.

Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); take limit; note positions of 1's.

Start with 1, apply 1->12, 21->21, 22->21, 2->2 (for final 2); take limit; note positions of 2's.

Expansion of the modular form of level 4 and weight 1/2.

a(n) = sigma_6(n), the sum of the 6th powers of the divisors of n.

a(n) = sigma_7(n), the sum of the 7th powers of the divisors of n.

a(n) = sigma_8(n), the sum of the 8th powers of the divisors of n.

a(n) = sigma_9(n), the sum of the 9th powers of the divisors of n.

a(n) = sigma_10(n), the sum of the 10th powers of the divisors of n.

a(n) = sigma_11(n), the sum of the 11th powers of the divisors of n.

a(n) = sigma_12(n), the sum of the 12th powers of the divisors of n.