A328558 - OEIS

%I #12 Sep 08 2022 08:46:24

%S 4,9,16,25,36,64,81,100,121,144,196,225,256,289,324,400,441,484,529,

%T 576,625,676,729,784,841,900,1024,1089,1156,1225,1296,1444,1521,1600,

%U 1681,1764,1936,2025,2116,2209,2304,2401,2500,2601,2704,2809,2916,3025,3136

%N Squares (A000290) that are not arithmetic numbers (A003601).

%C Numbers m such that the geometric 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 G(m) = sqrt(m) is an integer but A(m) = A000203(m) / A000005(m) is not an integer.

%C Corresponding values of G(m): 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, ...

%C Corresponding values of A(m): 7/3, 13/3, 31/5, 31/3, 91/9, 127/7, 121/5, 217/9, 133/3, 403/15, 133/3, 403/9, ...

%C Complement of A277793 with respect to A000290.

%t Select[Range[56]^2, !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* _Amiram Eldar_, Oct 20 2019 *)

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

%o (PARI) isA328558(n) = (issquare(n)&&(sigma(n)%numdiv(n))); \\ _Antti Karttunen_, Oct 19 2019

%Y Cf. A000005, A000203, A000290, A003601, A277793, A328557, A328559.

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Oct 19 2019