|
|
A325026
|
|
Multi-perfect numbers from A007691 that are not harmonic (A001599).
|
|
2
|
|
|
120, 523776, 1476304896, 31998395520, 518666803200, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 69357059049509038080, 87934476737668055040, 170206605192656148480, 1161492388333469337600, 1802582780370364661760, 1940351499647188992000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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).
|
|
LINKS
|
|
|
EXAMPLE
|
120 is a term because 120*tau(120)/sigma(120) = 120*16/360 = 16/3.
|
|
PROG
|
(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
|
|
CROSSREFS
|
Cf. A140798 (harmonic numbers that are not multi-perfect).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|