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%I #13 Sep 08 2022 08:46:24
%S 120,523776,459818240,1476304896,31998395520,51001180160,518666803200,
%T 30823866178560,740344994887680,796928461056000,212517062615531520,
%U 69357059049509038080,87934476737668055040,170206605192656148480,1161492388333469337600,1802582780370364661760
%N 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).
%C Numbers m such that m divides sigma(m) but sigma(m) does not divide m*(m-tau(m)).
%C Complement of A325023 with respect to A007691.
%e 120 is a term because 120*(120-tau(120))/sigma(120) = 120*(120-16)/360 = 104/3.
%t Select[Range[10^6], And[Mod[#3, #1] == 0, !IntegerQ[#1 (#1 - #2)/#3]] & @@ Prepend[DivisorSigma[{0, 1}, #], #] &] (* _Amiram Eldar_, Jul 10 2019 after _Michael De Vlieger_ at A325023 *)
%o (Magma) [n: n in [1..1000000] | not IsIntegral(((n-NumberOfDivisors(n)) * n) / SumOfDivisors(n)) and IsIntegral(SumOfDivisors(n)/n)]
%o (PARI) isA325024(m) = { my(s=sigma(m)); ((1==denominator(s/m)) && (1!=denominator(m*(m-numdiv(m))/s))); }; \\ _Antti Karttunen_, May 25 2019
%Y Cf. A000005, A000203, A007691, A049820, A325020, A325021, A325022, A325023.
%K nonn
%O 1,1
%A _Jaroslav Krizek_, May 12 2019
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