OFFSET
1,1
COMMENTS
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.
Numbers m such that neither A(m) = A000203(m)/A000005(m) nor H(m) = m * A000005(m)/A000203(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, ...
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
MAPLE
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:
select(filter, [$1..200]); # Robert Israel, Dec 14 2023
MATHEMATICA
Select[Range[180], !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] && !Divisible[# * DivisorSigma[0, #], DivisorSigma[1, #]] &] (* Amiram Eldar, Nov 01 2019 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Oct 31 2019
STATUS
approved