Sequences

Number of refactorable integers (A033950) of binary order (A029837) n.

The integer values of x/d(x) in order of magnitude of x in A033950.

Numbers k such that k*d(x) = x has no solution for x, where d (A000005) is the number of divisors; sequence gives impossible x/d(x) quotients in order of magnitude.

If n can be expressed as m/d(m) for some m, where d(m) is the number of divisors of m (A000005), then a(n) is the smallest such m, otherwise a(n) = 0.

Number of ordered rooted trees with n non-root nodes and all outdegrees <= three.

Number of ordered rooted trees with n non-root nodes and all outdegrees <= four.

Number of ordered rooted trees with n non-root nodes and all outdegrees <= five.

Number of ordered rooted trees with n non-root nodes and all outdegrees <= six.

Number of ordered rooted trees with n non-root nodes and all outdegrees <= seven.

Number of labeled rooted trees with a degree constraint: (2*n)!/(2^n) * C(2*n+1, n).

Number of labeled rooted trees with a degree constraint: ((3*n)!/(6^n)) * binomial(3*n + 1, n).

Number of labeled rooted trees with a degree constraint: ((4*n)!/(24^n)) * binomial(4*n+1, n).

Number of labeled rooted trees with a degree constraint: ((5*n)!/(120^n)) * C(5*n+1, n).

Number of labeled rooted unordered binary trees (each node has out-degree <= 2).

a(n) is the number of labeled rooted trees on a set of size n where each node has at most 3 neighbors that are further away from the root than the node itself.

a(n) is the number of labeled rooted trees on a set of size n where each node has at most 4 neighbors that are further away from the root than the node itself.

Number of labeled rooted trees with a degree constraint (described in the comments below).

Number of labeled rooted trees on 2n+1 nodes each node having an even number of children.

Greedy sequence such that no term is the average of three others.

Primes of the form n + Sum_{i=1..n} i!.

a(n) = n + Sum_{k=0..n} k!.

a(n) = n - 1 + Sum_{j=0..n} j!.

G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = tetragonal pyramid group of order 4 with cycle index (z1^5+2*z1*z4+z1*z2^2)/4.

G.f. satisfies A(x) = 1 + x*cycle_index(G,A(x)) where G = tetragonal pyramid group of order 8 with cycle index (z1^5+2*z1*z4+3*z1*z2^2+2*z1^3*z2)/8.

Numbers divisible by the squares of two distinct primes.

Length of Roman notation for n < length of decimal representation.

Length of Roman notation for n = length of decimal representation.

Length of Roman notation for n <= length of decimal representation.

a(n) = Sum_{i=0..n} floor((2*i + 2)/(n - i + 1)).

Continued fraction for Integral_{x=0..Pi} sin(x)/x.

Continued fraction for (2/Pi)*Integral_{x=0..Pi} sin(x)/x.

Decimal expansion of Integral_{x=0..Pi} (sin(x)/x) dx.

Decimal expansion of (2/Pi)*Integral_{x=0..Pi} sin(x)/x dx.

Number of sequences of length n with a_{i-1} < a_i <= a_1 + ... + a_{i-1} + 1.

Integers that can be decomposed into sums of different Fibonacci numbers of even argument.

Integers that can be decomposed into sums of different Fibonacci numbers of odd argument.

Iccanobif (or iccanobiF) primes: primes which are Fibonacci numbers when reversed.

Odd numbers m such that there exists an even number k < m with phi(k) = phi(m).

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

a(n) = -6 + 2^(n+1)*(3 - 2*n + n^2).

Number of partitions satisfying (cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

Number of partitions satisfying (cn(2,5) <= cn(1,5) and cn(3,5) <= cn(1,5) and cn(2,5) <= cn(4,5) and cn(3,5) <= cn(4,5)).

Number of partitions satisfying (cn(1,5) <= cn(2,5) and cn(1,5) <= cn(3,5) and cn(4,5) <= cn(2,5) and cn(4,5) <= cn(3,5)).

Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5)).

Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

Number of partitions satisfying (cn(0,5) = 0 and cn(2,5) <= cn(1,5) and cn(3,5) <= cn(1,5) and cn(2,5) <= cn(4,5) and cn(3,5) <= cn(4,5)).

Number of partitions satisfying (cn(0,5) <= cn(2,5) = cn(3,5) and cn(0,5) <= cn(1,5) and cn(0,5) <= cn(4,5)).

Number of partitions satisfying (cn(2,5) = cn(3,5) and cn(2,5) <= cn(1,5) and cn(2,5) <= cn(4,5)).

Number of partitions satisfying (cn(0,5) <= cn(1,5) = cn(4,5)).

Number of partitions satisfying (cn(1,5) = cn(4,5) and cn(0,5) <= cn(2,5) and cn(0,5) <= cn(3,5)).