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A369337
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Total number of numbers less than each divisor d of n that do not divide d.
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1
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0, 0, 1, 1, 3, 3, 5, 5, 7, 9, 9, 10, 11, 15, 15, 16, 15, 21, 17, 24, 23, 27, 21, 30, 25, 33, 30, 38, 27, 45, 29, 42, 39, 45, 39, 55, 35, 51, 47, 60, 39, 69, 41, 66, 60, 63, 45, 79, 51, 75, 63, 80, 51, 90, 63, 90, 71, 81, 57, 114, 59, 87, 86, 99, 75, 117, 65, 108, 87, 117, 69, 135, 71, 105
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OFFSET
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1,5
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LINKS
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FORMULA
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a(n) = Sum_{d|n} Sum_{k=1..d} ceiling(d/k) - floor(d/k).
a(n) = Sum_{k=1..n} Sum_{i=1..k} (ceiling(k/i) - floor(k/i)) * (1 - ceiling(n/k) + floor(n/k)).
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EXAMPLE
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a(12) = 10. The divisors of 12 are {1,2,3,4,6,12}. There are 0 numbers (positive integers) less than 1, 0 numbers less than 2 not dividing 2, 1 number less than 3 not dividing 3 (namely 2), 1 number less than 4 not dividing 4 (namely 3), 2 numbers less than 6 not dividing 6 (namely 4 and 5) and 6 numbers less than 12 not dividing 12 (namely 5,7,8,9,10,11).
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MATHEMATICA
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Table[Sum[Sum[(Ceiling[d/k] - Floor[d/k]), {k, d}], {d, Divisors[n]}], {n,
100}]
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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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