A360112 Number of solutions to m^(1 + 2^v(n-1)) == -m (mod n), where v(n) = A007814(n) is the 2-adic valuation of n, and 0 <= m < n.

2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 4, 3, 2, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 8, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 1, 8, 1, 4, 1, 4, 1, 4, 1, 4, 3, 4, 1, 4, 3, 4, 1, 4, 1, 8, 1, 4, 1, 2, 1, 8, 1, 4, 1, 8, 1, 4, 1, 4, 3, 4, 1, 8, 1, 4, 1, 4, 1, 8, 5, 4, 3, 4, 1, 8, 3, 4, 1, 4, 3, 4, 1, 4, 1, 4, 1, 8, 1, 4, 1, 4, 1, 4, 1, 8, 3, 4, 1, 8, 3, 4, 1, 4, 3, 8, 1

Offset

2,1

Links

Antti Karttunen, Table of n, a(n) for n = 2..16385

Prog

(PARI) A360112(n) = { my(f=factor(n), x = 1+(2^valuation(n-1, 2))); sum(m=0, n-1, !((m + m^x)%n)); };

Crossrefs

Cf. A007814, A345330 (composite numbers k, for which a(k) = 1), A345331 (odd numbers k, for which a(k) > 1), A360113, A360114 (positions of 1's).

Sequence in context: A135517 A327395 A327404 * A333570 A363320 A351032

Adjacent sequences: A360109 A360110 A360111 * A360113 A360114 A360115

Keyword

nonn

Author

Antti Karttunen, Feb 10 2023

Status

approved