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Numbers m with a divisor d such that tau(d) * sigma(d) = m.
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%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