A348091 For any positive number n, let f(n) be the infinite matrix (m_{i, j}, i, j > 0) with values in GF(2) encoding the Fermi-Dirac prime factors of n (n = Product_{i, j > 0} (prime(i)^2^(j-1))^m_{i, j}); let g be the inverse of f; a(n) = g(f(n)^2).

1, 2, 1, 1, 1, 6, 1, 8, 9, 10, 1, 18, 1, 14, 1, 1, 1, 18, 1, 25, 1, 22, 1, 108, 1, 26, 27, 49, 1, 30, 1, 32, 1, 34, 1, 36, 1, 38, 1, 1000, 1, 42, 1, 121, 9, 46, 1, 81, 1, 2, 1, 169, 1, 18, 1, 2744, 1, 58, 1, 450, 1, 62, 9, 1, 1, 66, 1, 289, 1, 70, 1, 18, 1, 74

Offset

1,2

Comments

We consider infinite matrices with finitely many nonzero entries; the square of these matrices is well defined. Also we operate on GF(2), all entries are 0 or 1.

There are infinitely many fixed points, for example the even squarefree numbers (A039956).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Rémy Sigrist, PARI program for A348091

Example

For n = 24:
- 24 = 2^2^0 * 2^2^1 * 3^2^0,
             [1 1 .]
- so f(24) = [1 0 .],
             [. . .]
            [0 1 .]
- f(24)^2 = [1 1 .],
            [. . .]
- a(24) = 2^2^1 * 3^2^0 * 3^2^1 = 108.

Prog

(PARI) See Links section.

Crossrefs

Cf. A039956, A050376.

Sequence in context: A351420 A331283 A060185 * A129110 A331562 A257101

Adjacent sequences: A348088 A348089 A348090 * A348092 A348093 A348094

Keyword

nonn,look

Author

Rémy Sigrist, Sep 29 2021

Status

approved