A330533 Multiply-perfect numbers m whose average divisor is not an integer.

28, 120, 496, 8128, 523776, 2178540, 33550336, 142990848, 459818240, 1379454720, 1476304896, 8589869056, 31998395520, 43861478400, 66433720320, 137438691328, 704575228896, 30823866178560, 181742883469056, 6088728021160320, 14942123276641920, 20158185857531904

Offset: 1

Author

Jaroslav Krizek, Dec 17 2019

Keywords

• nonn

Comments

Multiply-perfect numbers m such that A(m) = sigma(m) / tau(m) is not an integer. Corresponding values of A(m): 28/3, 45/2, 496/5, 8128/7, 98208/5, 121030/3, 33550336/13, 5957952/5, ...

Union of A046986 and A046987. Complement of A046985 with respect to A007691.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..307

Crossrefs

Cf. A007691, A046985, A046986, A046987.

Programs

Magma

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

Mathematica

Select[Range[10^6], Divisible[(s = DivisorSigma[1, #]), #] && !Divisible[s, DivisorSigma[0, #]] &] (* Amiram Eldar, Dec 19 2019 *)