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A066779
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Sum of squarefree numbers <= n.
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8
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1, 3, 6, 6, 11, 17, 24, 24, 24, 34, 45, 45, 58, 72, 87, 87, 104, 104, 123, 123, 144, 166, 189, 189, 189, 215, 215, 215, 244, 274, 305, 305, 338, 372, 407, 407, 444, 482, 521, 521, 562, 604, 647, 647, 647, 693, 740, 740, 740, 740, 791, 791, 844, 844, 899, 899
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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REFERENCES
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D. Suryanarayana, The number and sum of k-free integers <= x which are prime to n, Indian J. Math., Vol. 11 (1969), pp. 131-139.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} mu(i)^2*i.
a(n) ~ (3/Pi^2) * n^2 + O(n^(3/2)) (Suryanarayana, 1969). - Amiram Eldar, Mar 07 2021
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MATHEMATICA
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PROG
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(PARI) s=0; for (n=1, 1000, write("b066779.txt", n, " ", s+=moebius(n)^2*n) ) \\ Harry J. Smith, Mar 24 2010
(PARI) a(n)=my(s, k2); forsquarefree(k=1, sqrtint(n), k2=k[1]^2; s+= k2*binomial(n\k2+1, 2)*moebius(k)); s \\ Charles R Greathouse IV, Jan 08 2018
(Python)
from sympy.ntheory.factor_ import core
def a(n): return sum ([i for i in range(1, n + 1) if core(i) == i]) # Indranil Ghosh, Apr 16 2017
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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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