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A325026 Multi-perfect numbers from A007691 that are not harmonic (A001599). 1
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).

Supersequence of A046987.

Complement of A325025 with respect to A007691.

LINKS

Table of n, a(n) for n=1..15.

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. A000005, A000203, A001599, A007691, A325025.

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

Sequence in context: A181750 A003789 A325024 * A046987 A127232 A208191

Adjacent sequences:  A325023 A325024 A325025 * A325027 A325028 A325029

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Mar 24 2019

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)