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A325024
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Multiply-perfect numbers m from A007691 such that m*(m-tau(m))/sigma(m) is not an integer where k-tau(k) is the number of the non-divisors of k (A049820) and sigma(k) is the sum of the divisors of k (A000203).
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5
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120, 523776, 459818240, 1476304896, 31998395520, 51001180160, 518666803200, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 69357059049509038080, 87934476737668055040, 170206605192656148480, 1161492388333469337600, 1802582780370364661760
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OFFSET
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1,1
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COMMENTS
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Numbers m such that m divides sigma(m) but sigma(m) does not divide m*(m-tau(m)).
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LINKS
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EXAMPLE
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120 is a term because 120*(120-tau(120))/sigma(120) = 120*(120-16)/360 = 104/3.
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MATHEMATICA
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PROG
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(Magma) [n: n in [1..1000000] | not IsIntegral(((n-NumberOfDivisors(n)) * n) / SumOfDivisors(n)) and IsIntegral(SumOfDivisors(n)/n)]
(PARI) isA325024(m) = { my(s=sigma(m)); ((1==denominator(s/m)) && (1!=denominator(m*(m-numdiv(m))/s))); }; \\ Antti Karttunen, May 25 2019
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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