A143443 a(n) = n * A002321(n).

1, 0, -3, -4, -10, -6, -14, -16, -18, -10, -22, -24, -39, -28, -15, -16, -34, -36, -57, -60, -42, -22, -46, -48, -50, -26, -27, -28, -58, -90, -124, -128, -99, -68, -35, -36, -74, -38, 0, 0, -41, -84, -129, -132

Offset: 1

Author

Gary W. Adamson, Aug 15 2008

Keywords

• sign

Comments

Equals row sums of triangle A143442.

Examples

			First four terms = (1, 0, -3, -4) = (1*1, 2*0, 3*(-1), 4*(-1)), where the Mertens function A002321 = (1, 0, -1, -1, -2, -1, -2, -2, -2,...)
a(5) = -10 = sum of row 5 terms of triangle A143442: (5 - 5 - 5 + 0 - 5).
		

Crossrefs

Cf. A002321, A143442.

Programs

Mathematica

Table[n Plus @@ MoebiusMu[Range[n]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)

PARI

a(n) = n*sum(k=1, n, moebius(k)); \\ Michel Marcus, Aug 22 2015

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def A143443(n):
    if n == 0:
        return 0
    c, j = n, 2
    k1 = n//j
    while k1 > 1:
        j2 = n//k1 + 1
        c += (j2-j)*A143443(k1)//k1
        j, k1 = j2, n//j2
    return n*(j-c) # Chai Wah Wu, Mar 30 2021

Extensions

More terms from Carl Najafi, Aug 17 2011