A331668 Numbers m with a divisor d such that tau(d) * sigma(d) = m.

1, 6, 48, 168, 234, 336, 480, 720, 2688, 5760, 6048, 6552, 9920, 13104, 14880, 22932, 28080, 48384, 60480, 65520, 104832, 119040, 195840, 227584, 235872, 366912, 587520, 725760, 786240, 881280, 952320, 967680, 1048320, 2031120, 3641344, 3921372, 4642560

Offset: 1

Author

Jaroslav Krizek, Feb 28 2020

Keywords

• nonn

Comments

Corresponding values of divisors d: 1, 2, 6, 12, 18, 28, 24, 40, 84, 120, 224, 234, 496, 252, 240, 468, 360, 672, ...

Examples

			48 is a term because 6 divides 48, tau(6) = 4, sigma(6) = 12 and tau(6) * sigma(6) = 4 * 12 = 48.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..104

Crossrefs

Cf. A000005, A000203.

Programs

Magma

[n: n in [1..10^6] | #[d: d in Divisors(n) | NumberOfDivisors(d)*SumOfDivisors(d) eq n] ge 1];

Mathematica

seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #] * DivisorSigma[1, #] == n &]; Select[Range[70000], seqQ] (* Amiram Eldar, Feb 28 2020 *)

PARI

isok(m) = fordiv(m, d, if (sigma(d)*numdiv(d) == m, return (1))); \\ Michel Marcus, Mar 21 2020