A307740 Numbers k such that k divides lcm(tau(k), sigma(k)).

1, 2, 6, 12, 24, 28, 40, 84, 120, 252, 360, 496, 672, 2480, 3276, 4680, 7440, 8128, 30240, 32760, 56896, 293760, 435708, 523776, 997920, 2178540, 2618880, 8910720, 23569920, 33550336, 45532800, 64995840, 102136320, 142990848, 275890944, 436154368, 459818240

Offset: 1

Author

Jaroslav Krizek, Apr 26 2019

Keywords

• nonn

Comments

Numbers k such that k divides A009278(k).

Conjecture: multiply-perfect numbers (A007691) are terms.

Corresponding values of lcm(tau(k), sigma(k)) / k for numbers k from this sequence: 1, 3, 2, 7, 5, 6, 9, 8, 6, 26, 13, 10, 3, 12, 28, 14, 16, 14, 4, ...

Sequence of the smallest numbers k such that lcm(tau(k), sigma(k)) / k = n for n >= 1: 1, 6, 2, 30240, 24, 28, 12, 84, 40, 496, ...

Examples

			6 is in the sequence because lcm(tau(6), sigma(6)) / 6 = lcm(4, 12) / 6 = 12 / 6 = 2.
		

Crossrefs

Cf. A000005, A000203, A007691, A009278.

Programs

Magma

[n: n in [1..1000000] | LCM(SumOfDivisors(n), NumberOfDivisors(n)) mod n eq 0]

Mathematica

aQ[n_]:=Divisible[LCM@@(DivisorSigma[#,n]&/@{0,1}),n]; Select[Range[10000], aQ] (* Amiram Eldar, May 07 2019 *)

PARI

isok(n) = !(lcm(numdiv(n), sigma(n)) % n); \\ Michel Marcus, Apr 26 2019

Extensions

More terms from Amiram Eldar, May 07 2019