A325026 - OEIS

%I #14 May 10 2024 04:08:03

%S 120,523776,1476304896,31998395520,518666803200,30823866178560,

%T 740344994887680,796928461056000,212517062615531520,

%U 69357059049509038080,87934476737668055040,170206605192656148480,1161492388333469337600,1802582780370364661760,1940351499647188992000

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

%C 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).

%C Supersequence of A046987.

%C Complement of A325025 with respect to A007691.

%H Amiram Eldar, <a href="/A325026/b325026.txt">Table of n, a(n) for n = 1..202</a>

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

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

%o (PARI) isok(n) = my(s=sigma(n)); !frac(s/n) && frac(n*numdiv(n)/s); \\ _Michel Marcus_, Mar 24 2019

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

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

%K nonn

%O 1,1

%A _Jaroslav Krizek_, Mar 24 2019