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A271860
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a(n) = -Sum_{i=1..n} (-1)^floor(n/i).
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4
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0, 1, 0, 3, 0, 3, 2, 5, 0, 5, 4, 7, 2, 5, 4, 11, 4, 7, 6, 9, 4, 11, 10, 13, 4, 9, 8, 15, 10, 13, 12, 15, 6, 13, 12, 19, 12, 15, 14, 21, 12, 15, 14, 17, 12, 23, 22, 25, 12, 17, 16, 23, 18, 21, 20, 27, 18, 25, 24, 27, 18, 21, 20, 31, 20, 27, 26, 29, 24, 31, 30
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + x^k). - Seiichi Manyama, Jun 06 2021
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MAPLE
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MATHEMATICA
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Table[-Sum[(-1)^Floor[n/i], {i, n}], {n, 0, 100}]
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PROG
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(PARI) a(n) = -sum(i=1, n, (-1)^(n\i)); \\ Michel Marcus, Apr 16 2016
(PARI) my(N=99, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^k*(1-x^k)/(1+x^k))/(1-x))) \\ Seiichi Manyama, Jun 06 2021
(Python)
from math import isqrt
def A271860(n): return (((t:=isqrt(m:=n>>1))**2<<1)-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))-(sum(m//k for k in range(1, t+1))<<1)<<1)<<1)-n # Chai Wah Wu, Oct 23 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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