A328944 - OEIS

%I #13 Sep 08 2022 08:46:24

%S 3,5,7,11,13,14,15,17,19,20,21,22,23,27,29,30,31,33,35,37,38,39,41,42,

%T 43,44,45,46,47,49,51,53,54,55,56,57,59,60,61,62,65,66,67,68,69,70,71,

%U 73,77,78,79,83,85,86,87,89,91,92,93,94,95,96,97,99,101

%N Arithmetic numbers (A003601) that are not harmonic (A001599).

%C Numbers m such that the arithmetic mean of the divisors of m is an integer but the harmonic mean of the divisors of m is not an integer.

%C Numbers m such that A(m) = A000203(m)/A000005(m) is an integer but H(m) = m * A000005(m)/A000203(m) is not an integer.

%C Corresponding values of A(m): 2, 3, 4, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 21, 12, 22, ...

%C Corresponding values of H(m): 3/2, 5/3, 7/4, 11/6, 13/7, 7/3, 5/2, 17/9, 19/10, 20/7, 21/8, 22/9, ...

%C Complement of A007340 with respect to A003601.

%t Select[Range[100], Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] && !Divisible[# * DivisorSigma[0, #], DivisorSigma[1, #]] &] (* _Amiram Eldar_, Nov 01 2019 *)

%o (Magma) [m: m in [1..10^5] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(m * NumberOfDivisors(m) / SumOfDivisors(m))]

%Y Cf.: A000005, A000203, A003601, A007340, A046999, A328945.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Oct 31 2019