Sequences

Fully multiplicative with a(p) = [ (p+1)/2 ] for prime p.

Completely multiplicative with a(prime(k)) = prime(k+1).

Completely multiplicative with a(prime(k)) = floor( (prime(k+1)+1)/2 ) for k-th prime prime(k).

Fully multiplicative with a(p) = k if p is the k-th prime.

Fully multiplicative with a(prime(k)) = partition(k+1).

Fully multiplicative with a(prime(k)) = Fibonacci(k+2).

Möbius transform of A003958.

Inverse Möbius transform of A003958.

Möbius transform of A003959.

Inverse Möbius transform of A003959.

Möbius transform of A003960 (with alternating zeros omitted).

Inverse Möbius transform of A003960.

Moebius transform of A003961; a(n) = phi(A003961(n)), where A003961 shifts the prime factorization of n one step towards the larger primes.

Inverse Möbius transform of A003961; a(n) = sigma(A003961(n)), where A003961 shifts the prime factorization of n one step towards the larger primes.

Möbius transform of A003962.

Inverse Möbius transform of A003962.

Möbius transform of A003963 (with alternate 0's omitted).

Inverse Möbius transform of A003963.

Möbius transform of A003964.

Inverse Möbius transform of A003964.

Möbius transform of A003965.

Inverse Möbius transform of A003965.

Table read by rows: 1 if x = y, 0 otherwise, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...

Array read by antidiagonals with T(n,k) = min(n,k).

Table of max(x,y), where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...

Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is i AND j.

Table T(n,k) = n OR k read by antidiagonals.

Table of n XOR m (or Nim-sum of n and m) read by antidiagonals with m>=0, n>=0.

Triangle with subscripts (1,1),(2,1),(1,2),(3,1),(2,2),(1,3), etc. in which entry (i,j) is [ i/j ].

Triangle T from the array A(x, y) = gcd(x,y), for x >= 1, y >= 1, read by antidiagonals.

Table of lcm(x,y), read along antidiagonals.

Multiplication table read by antidiagonals: T(i,j) = i*j, i>=1, j>=1.

Square array read by upwards antidiagonals: T(n,k) = n^k for n >= 0, k >= 0.

Sequence b_3 (n) arising from homology of partitions with even number of blocks.

Sequence b_4 (n) arising from homology of partitions with even number of blocks.

Sum of (any number of) distinct squares: of form r^2 + s^2 + t^2 + ... with 0 <= r < s < t < ...

Sums of distinct nonzero squares in more than one way.

Sums of distinct positive cubes.

Numbers that are a sum of distinct positive cubes in more than one way.

Sums of distinct nonzero 4th powers.

RATS: Reverse Add Then Sort the digits applied to previous term, starting with 1.

Hofstadter-Conway $10000 sequence: a(n) = a(a(n-1)) + a(n-a(n-1)) with a(1) = a(2) = 1.

Benford numbers: a(n) = e^e^...^e (n times) rounded to nearest integer.

Number of domino tilings (or dimer coverings) of a 2n X 2n square.

a(n) = (3^(2*n+1) - 8*n - 3)/16.

Coefficients of elliptic function sn.

a(n) = C(n,1) + C(n,2) + C(n,3), or n*(n^2 + 5)/6.

Theta series of E_6 lattice.

Expansion of theta series of E_7 lattice in powers of q^2.

Expansion of Eisenstein series E_4(q) (alternate convention E_2(q)); theta series of E_8 lattice.