A086330 a(n) = Sum_{m >= 2} m! mod n.

0, 2, 4, 7, 2, 18, 8, 17, 12, 43, 8, 73, 32, 17, 24, 113, 26, 159, 12, 32, 76, 203, 8, 112, 164, 89, 60, 334, 32, 496, 88, 164, 232, 67, 44, 706, 292, 164, 32, 863, 74, 874, 164, 62, 456, 1097, 56, 291, 162, 317, 268, 1124, 116, 142, 88, 425, 566, 1560, 32, 2033, 930

Offset: 2

Author

Walter Carlini, Aug 31 2003

Keywords

• easy
• nonn

Comments

A discrete infinite sum that has some rough analogies to the infinite series for exponentials.

Examples

			a(7) = 2! mod 7 + 3! mod 7 + 4! mod 7 + 5! mod 7 + 6! mod 7 + 7! mod 7 + 8! mod 7 + . . . = 2 mod 7 + 6 mod 7 + 24 mod 7 + 120 mod 7 + 720 mod 7 + 5040 mod 7 + 40320 mod 7 + ... = 2 + 6 + 3 + 1 + 6 + (all further values are zero) = 18.
		

Crossrefs

Cf. A062169.

Programs

PARI

a(n) = sum(m=2, n, m! % n) \\ Michel Marcus, Jul 23 2013

Python

def A086330(n):
    a, c = 0, 1
    for m in range(2,n):
        c = c*m%n
        if c==0:
            break
        a += c
    return a # Chai Wah Wu, Apr 16 2024

Formula

a(n) = -1 + Sum_{k=1..n} A062169(n, k). - Vladeta Jovovic, Sep 06 2003

Extensions

Corrected and extended by Vladeta Jovovic, Sep 06 2003