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A328945
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Numbers m that are neither arithmetic (A003601) nor harmonic (A001599).
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2
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2, 4, 8, 9, 10, 12, 16, 18, 24, 25, 26, 32, 34, 36, 40, 48, 50, 52, 58, 63, 64, 72, 74, 75, 76, 80, 81, 82, 84, 88, 90, 98, 100, 104, 106, 108, 112, 117, 120, 121, 122, 124, 128, 130, 136, 144, 146, 148, 152, 156, 160, 162, 170, 171, 172, 175, 176, 178, 180
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OFFSET
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1,1
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COMMENTS
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Numbers m such that neither the arithmetic mean of the divisors of m nor the harmonic mean of the divisors of m is an integer.
Corresponding values of A(m): 3/2, 7/3, 15/4, 13/3, 9/2, 14/3, 31/5, 13/2, 15/2, 31/3, 21/2, 21/2, 27/2, ...
Corresponding values of H(m): 4/3, 12/7, 32/15, 27/13, 20/9, 18/7, 80/31, 36/13, 16/5, 75/31, 52/21, 64/21, ...
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LINKS
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MAPLE
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filter:= proc(n) local D, d, t;
D:=numtheory:-divisors(n);
d:= nops(D);
convert(D, `+`) mod d <> 0 and not ((d/add(1/t, t=D))::integer)
end proc:
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MATHEMATICA
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Select[Range[180], !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] && !Divisible[# * DivisorSigma[0, #], DivisorSigma[1, #]] &] (* Amiram Eldar, Nov 01 2019 *)
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PROG
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(Magma) [m: m in [1..10^5] | not IsIntegral(m * NumberOfDivisors(m) / SumOfDivisors(m)) and not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m))]
(PARI) isok(m) = my(f = factor(m), prd = sigma(f)/numdiv(f)); (denominator(prd) != 1) && (denominator(m/prd) != 1); \\ Michel Marcus, Nov 05 2019
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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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