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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Equals row sums of triangle A143442.
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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Table[n Plus @@ MoebiusMu[Range[n]], {n, 1, 80}] (* Carl Najafi, Aug 17 2011 *)
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PROG
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(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)
if n == 0:
return 0
c, j = n, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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