A277793 -id:A277793 - cp's OEIS frontend

A328557 Arithmetic numbers (A003601) that are not squares (A000290).

3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102

Offset: 1

Jaroslav Krizek, Oct 19 2019

nonn

Numbers m such that the arithmetic mean of the divisors of m is an integer but the geometric mean of the divisors of m is not an integer.
Numbers m such that A(m) = A000203(m) / A000005(m) is an integer but G(m) = sqrt(m) is not an integer.
Corresponding values of A(m): 2, 3, 3, 4, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 21, 12, 22, ...
Corresponding values of G(m): sqrt(3), sqrt(5), sqrt(6), sqrt(7), sqrt(11), sqrt(13), sqrt(14), sqrt(15), sqrt(17), ...
Complement of A277793 with respect to A003601.

Cf. A000005, A000203, A000290, A003601, A277793, A328558, A328559.

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

Select[Range[100], !IntegerQ @ Sqrt[#] && Divisible[DivisorSigma[1, #], DivisorSigma[0, #]] &] (* Amiram Eldar, Oct 20 2019 *)

isA328557(n) = (!issquare(n)&&!(sigma(n)%numdiv(n))); \\ Antti Karttunen, Oct 19 2019

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

Original entry on oeis.org

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

Jaroslav Krizek, Oct 19 2019

nonn

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.

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

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

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

isA328558(n) = (issquare(n)&&(sigma(n)%numdiv(n))); \\ Antti Karttunen, Oct 19 2019

cp's OEIS Frontend

A328557 Arithmetic numbers (A003601) that are not squares (A000290).

Views

Author

Keywords

Comments

Crossrefs

Programs

Magma

Mathematica

PARI