Sequences

Largest number whose base n representation does not repeat a pair of consecutive digits.

Largest number using only digits <= n that does not repeat a pair of consecutive digits.

Dirichlet convolution of powers of 2 (2,4,8,...) with themselves.

Dirichlet convolution of squares with themselves.

Dirichlet convolution of triangular numbers with themselves.

Dirichlet convolution of factorials with themselves.

Dirichlet convolution of Catalan numbers (1,2,5,14...) with themselves.

Dirichlet convolution of b_n=n with b_n with b_n.

Dirichlet convolution of powers of 3 (3,9,27,...) with themselves.

Number of different words that can be formed from an n X n grid of letters, reading horizontally, vertically or diagonally.

a(n) = (10*n^3 - 9*n^2 + 2*n)/3 + 1.

Products of successive Fibonacci numbers.

a(n) is the n-th sextic factorial number divided by 3.

a(n) = n-th sextic factorial number divided by 4.

Product of digits of A034686(n).

Smallest integral value of m/(sum of digits of m) for any n-digit number m.

a(n) = that n-digit number m which gives minimal integral value of m/(sum of digits of m); in case of a tie pick the smallest.

Sum of digits of A034727(n).

a(n) = Sum_{ k, k|n } 2^(k-1).

Dirichlet convolution of b_n=1 with c_n=3^(n-1).

Dirichlet convolution of b_n=1 with Catalan numbers.

Dirichlet convolution of b_n=1 with Bell numbers.

Dirichlet convolution of b_n=2^(n-1) with itself.

Dirichlet convolution of b_n=2^(n-1) with Fibonacci numbers.

Dirichlet convolution of b_n=2^(n-1) with c_n=3^(n-1).

Dirichlet convolution of b_n=2^(n-1) with Primes (with 1).

Dirichlet convolution of b_n=2^(n-1) with sigma(n).

Dirichlet convolution of b_n = 2^(n-1) with phi(n).

Dirichlet convolution of b_n=2^(n-1) with Catalan numbers.

Dirichlet convolution of b_n=2^(n-1) with Bell numbers.

Dirichlet convolution of mu(n) with 3^(n-1).

Dirichlet convolution of Moebius function mu(n) (A008683) with Catalan numbers (A000108).

a(n) = Sum_{d | n} mu(n/d) * Bell(d-1).

Dirichlet convolution of Fibonacci numbers with themselves.

Dirichlet convolution of Fibonacci numbers with 3^(n-1).

Dirichlet convolution of Fibonacci numbers with Primes (with 1).

Dirichlet convolution of Fibonacci numbers with sigma(n).

Dirichlet convolution of Fibonacci numbers with phi(n).

Dirichlet convolution of Fibonacci numbers with Catalan numbers.

Dirichlet convolution of Fibonacci numbers with Bell numbers.

Dirichlet convolution of 3^(n-1) with itself.

Dirichlet convolution of 3^(n-1) with primes (with 1).

Dirichlet convolution of 3^(n-1) with sigma(n).

Dirichlet convolution of 3^(n-1) with phi(n).

Dirichlet convolution of 3^(n-1) with Catalan numbers.

Dirichlet convolution of 3^(n-1) with Bell numbers.

a(1)=1, a(n) = smallest odd number such that all sums of pairs of (not necessarily distinct) terms in the sequence are distinct.

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

Dirichlet convolution of primes (with 1) with themselves.

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