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

1,1

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

Table of n, a(n) for n=1..22.

Mathematica

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

Prog

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

Crossrefs

Cf. A007691, A046985, A046986, A046987.

Sequence in context: A233372 A220755 A244079 * A363253 A101095 A232403

Adjacent sequences: A330530 A330531 A330532 * A330534 A330535 A330536

Keyword

nonn

Author

Jaroslav Krizek, Dec 17 2019

Status

approved