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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..66.

Mathematica

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

Prog

(Magma) [m: m in [1..10^5] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(m))]
(PARI) isA328557(n) = (!issquare(n)&&!(sigma(n)%numdiv(n))); \\ Antti Karttunen, Oct 19 2019

Crossrefs

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

Sequence in context: A064728 A046839 A003601 * A216782 A328952 A072600

Adjacent sequences: A328554 A328555 A328556 * A328558 A328559 A328560

Keyword

nonn

Author

Jaroslav Krizek, Oct 19 2019

Status

approved