A325026 Multi-perfect numbers from A007691 that are not harmonic (A001599).

120, 523776, 1476304896, 31998395520, 518666803200, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 69357059049509038080, 87934476737668055040, 170206605192656148480, 1161492388333469337600, 1802582780370364661760, 1940351499647188992000

Offset: 1

Author

Jaroslav Krizek, Mar 24 2019

Keywords

• nonn

Comments

Multi-perfect numbers m such that m*tau(m)/sigma(m) is not an integer, where tau(k) is the number of the divisors of k (A000005) and sigma(k) is the sum of the divisors of k (A000203).

Supersequence of A046987.

Complement of A325025 with respect to A007691.

Examples

			120 is a term because 120*tau(120)/sigma(120) = 120*16/360 = 16/3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..202

Crossrefs

Cf. A000005, A000203, A001599, A007691, A325025.

Cf. A140798 (harmonic numbers that are not multi-perfect).

Programs

Magma

[n: n in [1..1000000] | not IsIntegral((NumberOfDivisors(n)) * n / SumOfDivisors(n)) and IsIntegral(SumOfDivisors(n)/n)]

PARI

isok(n) = my(s=sigma(n)); !frac(s/n) && frac(n*numdiv(n)/s); \\ Michel Marcus, Mar 24 2019