A328953 - OEIS

%I #11 Sep 08 2022 08:46:24

%S 4,9,16,25,36,50,64,81,100,117,121,144,180,196,200,225,242,256,289,

%T 324,325,400,441,450,468,484,529,576,578,625,650,676,729,784,800,841,

%U 900,968,1024,1058,1089,1156,1225,1280,1296,1300,1444,1476,1521,1600,1620

%N Antiharmonic numbers (A020487) that are not arithmetic (A003601).

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

%C Numbers m such that B(m) = A001157(m) / A000203(m) is an integer but A(m) = A000203(m) / A000005(m) is not an integer.

%C Corresponding values of B(m): 3, 7, 11, 21, 21, 35, 43, 61, 63, 85, 111, 77, 91, 129, 119, 147, 185, 171, 273, 183, ...

%C Corresponding values of A(m): 7/3, 13/3, 31/5, 31/3, 91/9, 31/2, 127/7, 121/5, 217/9, 91/3, 133/3, ...

%t Select[Range[1620], !Divisible[(sigma = DivisorSigma[1, #]), DivisorSigma[0, #]] && Divisible[DivisorSigma[2, #], sigma] &] (* _Amiram Eldar_, Nov 17 2019 *)

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

%Y Complement of A277553 with respect to A020487.

%Y Cf. A000005, A000203, A001157, A003601, A328952, A328954.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Nov 17 2019