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

1,2

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, ...

Links

Table of n, a(n) for n=1..37.

Example

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

Mathematica

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

Prog

(Magma) [n: n in [1..1000000] | LCM(SumOfDivisors(n), NumberOfDivisors(n)) mod n eq 0]
(PARI) isok(n) = !(lcm(numdiv(n), sigma(n)) % n); \\ Michel Marcus, Apr 26 2019

Crossrefs

Cf. A000005, A000203, A007691, A009278.

Sequence in context: A323950 A291014 A257479 * A244043 A058868 A129314

Adjacent sequences: A307737 A307738 A307739 * A307741 A307742 A307743

Keyword

nonn

Author

Jaroslav Krizek, Apr 26 2019

Extensions

More terms from Amiram Eldar, May 07 2019

Status

approved