%I #11 Sep 08 2022 08:46:25
%S 1,6,48,168,234,336,480,720,2688,5760,6048,6552,9920,13104,14880,
%T 22932,28080,48384,60480,65520,104832,119040,195840,227584,235872,
%U 366912,587520,725760,786240,881280,952320,967680,1048320,2031120,3641344,3921372,4642560
%N Numbers m with a divisor d such that tau(d) * sigma(d) = m.
%C Corresponding values of divisors d: 1, 2, 6, 12, 18, 28, 24, 40, 84, 120, 224, 234, 496, 252, 240, 468, 360, 672, ...
%e 48 is a term because 6 divides 48, tau(6) = 4, sigma(6) = 12 and tau(6) * sigma(6) = 4 * 12 = 48.
%t seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #] * DivisorSigma[1, #] == n &]; Select[Range[70000], seqQ] (* _Amiram Eldar_, Feb 28 2020 *)
%o (Magma) [n: n in [1..10^6] | #[d: d in Divisors(n) | NumberOfDivisors(d)*SumOfDivisors(d) eq n] ge 1]
%o (PARI) isok(m) = fordiv(m, d, if (sigma(d)*numdiv(d) == m, return (1))); \\ _Michel Marcus_, Mar 21 2020
%Y Cf. A000005, A000203.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Feb 28 2020