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 A245782 Refactorable multiply-perfect numbers. 5
 1, 672, 30240, 23569920, 45532800, 14182439040, 153003540480, 403031236608, 518666803200, 13661860101120, 740344994887680, 796928461056000, 212517062615531520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Multiply-perfect numbers n (A007691) such that n / tau(n) is integer. Also multiply-perfect numbers n (A007691) such that (n / tau(n) - sigma(n) / n) = (n / A000005(n) - A000203(n) / n) is integer. Also multiply-perfect numbers n (A007691) such that (n / tau(n) + sigma(n) / n) = (n / A000005(n) + A000203(n) / n) is integer. Subsequence of A245778 and A245786. Supersequence of A047728. Intersection of A033950 (refactorable numbers) and A007691 (multiply-perfect numbers). LINKS EXAMPLE Multiply-perfect number 672 is in sequence because 672 / tau(672) = 28 (integer). PROG (MAGMA) [n:n in [A007691(n)] | (Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) eq 1] (PARI) isok(n) = !(n % numdiv(n)) && !(sigma(n) % n); \\ Michel Marcus, Aug 11 2014 CROSSREFS Cf. A000005, A000203, A007691, A047728. Cf. A245776, A245777, A245778, A245779, A245786. Sequence in context: A321116 A234481 A234476 * A047728 A297123 A160209 Adjacent sequences:  A245779 A245780 A245781 * A245783 A245784 A245785 KEYWORD nonn,more AUTHOR Jaroslav Krizek, Aug 01 2014 STATUS approved

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Last modified February 21 23:29 EST 2019. Contains 320381 sequences. (Running on oeis4.)