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A245782
Refactorable multiply-perfect numbers.
8
1, 672, 30240, 23569920, 45532800, 14182439040, 153003540480, 403031236608, 518666803200, 13661860101120, 740344994887680, 796928461056000, 212517062615531520, 87934476737668055040, 154345556085770649600, 170206605192656148480, 1161492388333469337600, 1802582780370364661760
OFFSET
1,2
COMMENTS
Multiply-perfect numbers k (A007691) such that k / tau(k) is integer.
Also multiply-perfect numbers k (A007691) such that (k / tau(k) - sigma(k) / k) = (k / A000005(k) - A000203(k) / k) is integer.
Also multiply-perfect numbers k (A007691) such that (k / tau(k) + sigma(k) / k) = (k / A000005(k) + A000203(k) / k) is integer.
LINKS
EXAMPLE
Multiply-perfect number 672 is in sequence because 672 / tau(672) = 28 (integer).
MATHEMATICA
q[n_] := Module[{d = DivisorSigma[0, n], s = DivisorSigma[1, n]}, Divisible[s, n] && Divisible[n, d]]; Select[Range[31000], q] (* Amiram Eldar, May 09 2024 *)
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
(PARI) is(k) = {my(f = factor(k), s = sigma(f), d = numdiv(f)); !(s % k) && !(k % d); } \\ Amiram Eldar, May 09 2024
CROSSREFS
Intersection of A033950 (refactorable numbers) and A007691 (multiply-perfect numbers).
Subsequence of A245778 and A245786.
Supersequence of A047728.
Sequence in context: A234476 A340864 A331666 * A047728 A297123 A335254
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Aug 01 2014
EXTENSIONS
a(14)-a(18) from Amiram Eldar, May 09 2024
STATUS
approved