OFFSET
1,2
COMMENTS
Multiply-perfect numbers m such that values A(m) = sigma(m)/tau(m) = A000203(m)/A000005(m) are any integers.
Corresponding values of A(m): 1, 3, 84, 1260, 1365, 294624, 474300, 36933435, 318757376, 637514752, 1199497728, ...
Has many terms in common with B = {multiply perfect numbers n divisible by bigomega(n)}: only {1, 45532800, 403031236608, 212517062615531520, ...} are in {a(n)} \ B, while {120, 523776, 2178540, ...} are in B \ {a(n)}. - M. F. Hasler, Jan 31 2020
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..423
EXAMPLE
sigma(672)/tau(672) = 2016/24 = 84 (integers).
MATHEMATICA
seqQ[n_] := And @@ (Divisible[DivisorSigma[1, n], #] & /@ {n, DivisorSigma[0, n]}); Select[Range[5*10^7], seqQ] (* Amiram Eldar, Jan 25 2020 *)
PROG
(Magma) [m: m in [1..10^7] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and IsIntegral(SumOfDivisors(m) / m)]
(PARI) is_A331724(n)={my(f=factor(n), s=sigma(f)); !(s%n||s%numdiv(f))} \\ M. F. Hasler, Jan 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 25 2020
STATUS
approved