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A069891
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Sum_{k=1..n} A007913(k), the squarefree part of k.
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3
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0, 1, 3, 6, 7, 12, 18, 25, 27, 28, 38, 49, 52, 65, 79, 94, 95, 112, 114, 133, 138, 159, 181, 204, 210, 211, 237, 240, 247, 276, 306, 337, 339, 372, 406, 441, 442, 479, 517, 556, 566, 607, 649, 692, 703, 708, 754, 801, 804, 805, 807, 858, 871, 924, 930, 985, 999
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Sum{1<=k<=n,k squarefree} (1/k) = Sum{1<=k<=n} (mu(k)^2/k) = (1/zeta(2))*(ln(n)+gamma-2*zeta'(2)/zeta(2))+O(1/sqrt(n)) (Suryanarayana)
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REFERENCES
| Suryanarayana, D. Asymptotic formula for sum_{n <= x} mu^{2}(n)/n, Indian J. Math. 9 (1967/1968) 543-545.
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FORMULA
| a(n) is the sum from d=1 to sqrt(n) of f(d)*C(floor(n/d^2)+1, 2) where f(d)=A046970(d) is the product of 1-p^2 over all prime divisors p of d and C(r, s) is the binomial coefficient r choose s.
a(n) is asymptotic to r*n^2, where r = pi^2/30 = 0.3289868...
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MATHEMATICA
| a[n_] := Sum[Times@@(1-#1[[1]]^2&)/@FactorInteger[d]*Binomial[Floor[n/d^2]+1, 2], {d, 1, Floor[Sqrt[n]]}]
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CROSSREFS
| Cf. A069087.
Sequence in context: A189634 A047705 A169799 * A190118 A175048 A088146
Adjacent sequences: A069888 A069889 A069890 * A069892 A069893 A069894
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KEYWORD
| nonn
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AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Apr 09 2002
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