Sequences

Dirichlet convolution of sigma(n) with itself.

Dirichlet convolution of primes (with 1) with sigma(n).

Dirichlet convolution of primes (with 1) with Catalan numbers.

Dirichlet convolution of sigma(n) with Catalan numbers.

Dirichlet convolution of sigma(n) with Bell numbers.

Dirichlet convolution of phi(n) with Catalan numbers.

Dirichlet convolution of phi(n) with Bell numbers.

Dirichlet convolution of Catalan numbers with themselves.

Dirichlet convolution of Catalan numbers with Bell numbers.

Dirichlet convolution of Bell numbers with themselves.

Dirichlet convolution of d(n) (# of divisors) with b_n=2^(n-1).

Dirichlet convolution of d(n) (number of divisors) with Fibonacci numbers.

Dirichlet convolution of d(n) (number of divisors of n) with primes (with 1).

Dirichlet convolution of d(n) (# of divisors) with Catalan numbers.

Dirichlet convolution of d(n) (# of divisors) with Bell numbers.

Gozinta numbers: possible number of gozinta chains for some positive integer.

Dirichlet convolution of [ 1,1,1,... ] with Ramanujan numbers (A000594).

Dirichlet convolution of Ramanujan numbers (A000594) with themselves.

Dirichlet convolution of [ 1,1,1,... ] with A034778.

Numbers k such that A034693(k) = 4.

Triangle of number of rooted trees with n >= 2 nodes and height h >= 1.

Numbers n such that A034693(n) = 3: 3n + 1 is prime, but neither n + 1 nor 2n + 1.

Numbers k such that A034693(k) = 6.

Numbers n such that A034693(n) = 2.

a(n) = 2^(n-th prime).

Number of linearly ordered Girard monoids of size n; number of t-norms on an n-chain inducing an involutive residual negator.

a(n) = n-th sextic factorial number divided by 5.

a(n) is the n-th sextic factorial number divided by 6.

Related to sextic factorial numbers A008542.

Erroneous version of A000602.

a(n) is square mod a(i), i < n.

Lexicographically earliest sequence of pairwise coprime triangular numbers.

a(1)=1; thereafter a(n+1) is the least k > a(n) such that k is a square mod a(i) for all i<= n.

a(n) is the least prime p > a(n-1) such that a(n-1) is a quadratic residue mod p.

a(n) is the least prime > a(n-1) that is a quadratic residue mod a(n-1).

a(1)=1, a(n-1) is a square mod a(n), and a(n) > a(n-1).

a(0) = 0; a(n+1) = a(n) + 2^a(n).

Value of n considered as a game.

Triangle read by rows: T(n,k) is the number of partially labeled trees with n nodes, k of which are labeled, 0 <= k <= n.

Triangle of number of node labeled trees by number of nodes and number of labels.

Triangle of Fibonomial coefficients (k=2).

Triangle of Fibonomial coefficients (k=3).

Consider the sequence of 4-tuples {0,a,b,c} (c>=a+b; a,b,c>0) which have the smallest integer 'c' required to reach {k,k,k,k} in n steps under map {r,s,t,u}->{|r-s|,|s-t|,|t-u|,|u-r|}. This sequence gives the second term 'a' of these quadruples.

Consider the sequence of 4-tuples {0,a,b,c} (c>=a+b; a,b,c>0) which have the smallest integer 'c' required to reach {k,k,k,k} in n steps under map {r,s,t,u}->{|r-s|,|s-t|,|t-u|,|u-r|}. This sequence gives the third term 'b' of these quadruples.

Erroneous version of A000022.

Number of distinct sets of 2 numbers > 1 such that their product is between n^2 and (n+1)^2.

Triangle T(n,k) of coefficients of Lucas (or Cardan) polynomials.

Concatenation of 'prevprime(k) and k' is a prime.

Numbers k such that the concatenation of k and previous_prime(k) is a prime.

Concatenation of 'prevprime(k) and k and nextprime(k)' is a prime.