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A266227
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a(n) = floor(Sum_{d|n} 1/sigma(d)).
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9
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1
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OFFSET
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1,60
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COMMENTS
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Sequence of numbers n such that floor(Sum_{d|n} 1/sigma(d)) = k for k = 1, 2, 3:
k = 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ... (A265711);
k = 2: 60, 72, 84, 90, 120, 144, 168, 180, 210, 216, 240, 252, ... (A265712);
k = 3: 110880, 166320, 221760, 277200, 327600, 332640, 360360, ... (A265713).
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LINKS
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FORMULA
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a(n) = floor(Sum_{d|n} 1/A000203(d)).
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EXAMPLE
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For n = 6; a(6) = floor(Sum_{d|6} 1/sigma(d)) = floor(1/1 + 1/3 + 1/4 + 1/12) = floor(5/3) = 1.
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MATHEMATICA
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A266227[n_] := Floor[DivisorSum[n, 1/DivisorSigma[1, #]&]];
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PROG
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(Magma) [Floor(&+[1/SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) A266227(n) = { my(s=sumdiv(n, d, 1/sigma(d))); (numerator(s) \ denominator(s)); }; \\ Antti Karttunen, Nov 19 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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