A328558 Squares (A000290) that are not arithmetic numbers (A003601).

4, 9, 16, 25, 36, 64, 81, 100, 121, 144, 196, 225, 256, 289, 324, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 1024, 1089, 1156, 1225, 1296, 1444, 1521, 1600, 1681, 1764, 1936, 2025, 2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136

Offset

1,1

Comments

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.

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

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, ...

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, ...

Complement of A277793 with respect to A000290.

Links

Table of n, a(n) for n=1..49.

Mathematica

Select[Range[56]^2, !Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Oct 20 2019 *)

Prog

(Magma) [m: m in [1..10^5] | not IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and IsIntegral(Sqrt(m))]
(PARI) isA328558(n) = (issquare(n)&&(sigma(n)%numdiv(n))); \\ Antti Karttunen, Oct 19 2019

Crossrefs

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

Sequence in context: A235597 A309002 A328953 * A072862 A300303 A062295

Adjacent sequences: A328555 A328556 A328557 * A328559 A328560 A328561

Keyword

nonn

Author

Jaroslav Krizek, Oct 19 2019

Status

approved