A342403 a(1) = 1; a(n) = -Sum_{d|n, d < n} d * a(d).

1, -1, -1, 1, -1, 4, -1, -3, 2, 6, -1, -24, -1, 8, 7, 21, -1, -38, -1, -58, 9, 12, -1, 288, 4, 14, -16, -108, -1, -180, -1, -315, 13, 18, 11, 930, -1, 20, 15, 1126, -1, -314, -1, -256, -116, 24, -1, -6960, 6, -154, 19, -354, -1, 1078, 15, 2940, 21, 30, -1, 6664, -1, 32, -198, 9765, 17

Offset: 1

Author

Ilya Gutkovskiy, Mar 10 2021

Keywords

• sign

Links

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

Crossrefs

Cf. A008683, A055615, A165552, A321384.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = -Sum[d a[d], {d, Most @ Divisors[n]}]; Table[a[n], {n, 1, 65}]

PARI

a(n) = if (n==1, 1, -sumdiv(n, d, if (dMichel Marcus, Mar 11 2021

PARI

up_to = 20000;
A342403list(n) = { my(v=vector(n)); v[1] = 1; for(n=2, #v, v[n] = -sumdiv(n, d, if(d==n, 0, v[d]*d))); (v); };
v342403 = A342403list(up_to);
A342403(n) = v342403[n]; \\ Antti Karttunen, Jan 22 2025

Python

from sympy import divisors
def A342403(n): return 1 if n == 1 else -sum(d*A342403(d) for d in divisors(n) if d < n) # Chai Wah Wu, Mar 11 2021