A336322 a(n) = A225546(A122111(n)).

1, 2, 3, 4, 6, 8, 5, 16, 9, 12, 10, 32, 15, 24, 18, 256, 30, 64, 7, 48, 27, 20, 14, 512, 36, 40, 81, 96, 21, 128, 42, 65536, 54, 60, 72, 1024, 35, 120, 45, 768, 70, 192, 105, 80, 162, 28, 210, 131072, 25, 144, 90, 160, 11, 4096, 108, 1536, 135, 56, 22, 2048, 33, 84, 243, 4294967296, 216, 384, 66, 240, 270, 288, 55, 262144, 110, 168, 324, 480, 50

Offset: 1

Author

Antti Karttunen and Peter Munn, Jul 17 2020

Keywords

• nonn

Comments

A225546 and A122111 are both self-inverse permutations of the positive integers based on prime factorizations, and they share further common properties. For instance, they map the prime numbers to powers of 2: A225546 maps the k-th prime to 2^2^(k-1), whereas A122111 maps it to 2^k.

In composing these permutations, this sequence maps the list of prime numbers to the squarefree numbers, as listed in A019565; and the "normal" numbers (A055932), as listed in A057335, to ascending powers of 2.

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

A225546 composed with A122111.

Sorted even bisection: A335738.

Sorted odd bisection (excluding 1): A335740.

Sequences used to express relationship between terms of this sequence: A001222, A003961, A253560, A331590, A350066.

Sequences of sequences (S_1, S_2, ... S_j) with the property a(S_i) = S_{i+1}, or essentially so: (A033844, A000040, A019565), (A057335, A000079, A001146), (A000244, A011764), (A001248, A334110), (A253563, A334866).

The inverse permutation, A336321, lists sequences where the property is weaker (between the sets of terms).

Formula

a(A033844(m)) = A000040(m+1). [Offset corrected Peter Munn, Feb 14 2022]

a(A000040(m)) = A019565(m).

a(A057335(m)) = 2^m.

For m >= 1, a(2^m) = A001146(m-1).

a(A253563(m)) = A334866(m).

From Peter Munn, Feb 14 2022: (Start)

a(A253560(n)) = a(n)^2.

For n >= 2, a(A003961(n)) = A331590(a(n), 2^2^(A001222(n)-1)).

a(A350066(n, k)) = A331590(a(n), a(k)).

(End)