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A256102
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Numbers m such that gcd(A001008(m), m) > 1, in increasing order.
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5
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20, 42, 77, 110, 156, 272, 342, 506, 812, 930, 1247, 1332, 1640, 1806, 2162, 2756, 3422, 3660, 4422, 4970, 5256, 6162, 6806, 7832, 9312, 9328, 10100, 10506, 11342, 11772, 12656, 16002, 17030, 18632, 19182, 22052, 22650, 24492, 26406, 27722, 29756, 31862, 32580, 36290, 37056, 38612, 39402
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OFFSET
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1,1
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COMMENTS
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For the corresponding values of GCD(A001008(a(n)), a(n)) see A256103(n).
This means that for all values n not in the present sequence the numerator of the harmonic sum (HS) of the first n positive integers coincides with the denominator of the harmonic mean (HM) of the first n positive integers. That is, n divides the HM(n) numerator A102928(n) for n not in the present sequence.
All terms are composite. Sequences contains all numbers of the form p*(p - 1), where p is a prime >= 5. This is because p^2 divides numerator(Sum_{i=1..p-1) 1/(k*p + i)), and p divides numerator(Sum_{i=1..p-1} 1/(i*p)), so p divides numerator(Sum_{i=1..p*(p-1)} 1/i). - Jianing Song, Dec 24 2018
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LINKS
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FORMULA
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a(n) is the n-th smallest element of the set M:= {m positive inter | gcd(A001008(m), m) > 1}, n >= 1.
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EXAMPLE
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Because 19 is not in this sequence 1 = gcd(A001008(19), 19) = gcd(275295799, 19).
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MATHEMATICA
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Select[Range[10^4], !CoprimeQ[#, Numerator @ HarmonicNumber[#]] &] (* Amiram Eldar, Feb 24 2020 *)
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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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