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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
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
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
Sequence in context: A351420 A331283 A060185 * A129110 A331562 A257101
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Sep 29 2021
STATUS
approved