Sequences

Take sum of squares of digits of previous term.

Take sum of squares of digits of previous term; start with 8.

Take sum of squares of digits of previous term; start with 9.

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

2^(2n-6) * C(n,3) - 2^(n-2) * C(n,4).

a(n) = 2^n - Fibonacci(n+2).

a(n) = n OR n^2 (applied to ternary expansions).

a(n) = n OR n^3 (applied to binary expansions).

a(n) = n OR n^3 (applied to ternary expansions).

At least 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.

Exactly 3 out of 10m+1, 10m+3, 10m+7, 10m+9 are primes.

Sum of the distinct primes dividing n.

If n = Product (p_j^k_j) then a(n) = Product (p_j + k_j).

If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j).

If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 0 by convention).

If n = Product (p_j^k_j) then a(n) = Sum (k_j^p_j).

If n = Product (p_j^k_j) then a(n) = Product (k_j^p_j).

Integers of the form Product p_j^k_j = Product k_j^p_j; p_j in A000040.

Number of numbers <= n with same prime factors as n.

Number of ordered prime factorizations of n.

If n = Product (p_j^k_j) then a(n) = Sum partition(k_j).

Coefficients in expansion of (x-1)*(1+x)^(n-1), n > 0.

Number of partitions of n into parts >= 3.

Number of partitions of n into parts >= 4.

Coefficient of x^n in Product_{k>=1} 1/(1-x^k)^n.

Expansion of (1 + x + x^2)/(1 - x)^2.

Expansion of (1-x^5) / (1-x)^5.

Expansion of (1-x^6) / (1-x)^6.

Expansion of (1-x^7)/(1-x)^7.

Expansion of (1-x^8) / (1-x)^8.

Expansion of (1-x^9 ) / (1-x)^9.

Expansion of (1-x^10) / (1-x)^10.

Expansion of (1-x^11) / (1-x)^11.

Expansion of (1-x^12) / (1-x)^12.

Expansion of (1-x^13) / (1-x)^13.

a(n) = floor(n/5)*floor((n+1)/5)*floor((n+2)/5).

a(n) = floor(n/5)*floor((n+1)/5).

4-dimensional centered tetrahedral numbers.

Number of 5-dimensional centered tetrahedral numbers.

6-dimensional centered tetrahedral numbers.

7-dimensional centered tetrahedral numbers.

8-dimensional centered tetrahedral numbers.

9-dimensional centered tetrahedral numbers.

10-dimensional centered tetrahedral numbers.

11-dimensional centered tetrahedral numbers.

12-dimensional centered tetrahedral numbers.

Number of odd composite numbers less than n-th odd prime.

Number of odd primes less than n-th odd composite number.

Positive integers k such that k-th triangular number is palindromic.

Numbers k such that both k and the k-th triangular number are palindromes.