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

Author

Antti Karttunen, Feb 10 2023

Keywords

• nonn

Links

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

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).

Programs

PARI

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