A328954 - OEIS

%I #9 Sep 08 2022 08:46:24

%S 2,8,10,12,18,24,26,28,32,34,40,48,52,58,63,72,74,75,76,80,82,84,88,

%T 90,98,104,106,108,112,120,122,124,128,130,136,146,148,152,156,160,

%U 162,170,171,172,175,176,178,192,194,202,208,216,218,226,228,232,234

%N Numbers m that are neither arithmetic (A003601) nor antiharmonic (A020487).

%C Numbers m such that neither the arithmetic mean of the divisors of m nor the antiharmonic mean of the divisors of m is an integer.

%C Numbers m such that neither A(m) = A000203(m)/A000005(m) nor B(m) = A001157(m)/A000203(m) is an integer.

%C Corresponding values of A(m): 3/2, 15/4, 9/2, 14/3, 13/2, 15/2, 21/2, 28/3, 21/2, 27/2, 45/4, 62/5, ...

%C Corresponding values of B(m): 5/3, 17/3, 65/9, 15/2, 35/3, 85/6, 425/21, 75/4, 65/3, 725/27, 221/9, ...

%t Select[Range[235], !Divisible[DivisorSigma[2, #], (s = DivisorSigma[1, #])] && !Divisible[s, DivisorSigma[0, #]] &] (* _Amiram Eldar_, Dec 06 2019 *)

%o (Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(&+[d^2: d in Divisors(m)] / SumOfDivisors(m))]

%Y Cf. A000005, A000203, A001157, A003601, A277553, A328952, A328953.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Dec 03 2019