A323652 Numbers m having at least one divisor d such that m divides sigma(d).

1, 6, 12, 28, 56, 120, 360, 496, 672, 992, 2016, 8128, 16256, 30240, 32760, 60480, 65520, 120960, 131040, 523776, 1571328, 2178540, 4357080, 8714160, 23569920, 33550336, 45532800, 47139840, 67100672, 91065600, 94279680, 142990848, 182131200, 285981696

Offset

1,2

Comments

Generalization of multiperfect numbers (A007691).

Multiperfect numbers (A007691) are terms. If m is a k-multiperfect number and d divides k (for k > 1 and d > 1), then d*m is also a term.

Number 1379454720 is the smallest number with two divisors d with this property (459818240 and 1379454720). Another such number is 153003540480 with divisors 51001180160 and 153003540480. Is there a number with three divisors d with this property?

Supersequence of A081756.

Links

Table of n, a(n) for n=1..34.

Example

12 is a term because 6 divides 12 and simultaneously 12 divides sigma(6) = 12.

Mathematica

Select[Range[530000], AnyTrue[DivisorSigma[1, Divisors[#]]/#, IntegerQ]&] (* The program generates the first 20 terms of the sequence. To generate more, increase the Range constant, but the program may take a long time to run. *) (* Harvey P. Dale, Jan 17 2022 *)

Prog

(Magma) [n: n in [1..10000] | #[d: d in Divisors(n) | SumOfDivisors(d) mod n eq 0] gt 0]
(PARI) isok(n) = {fordiv(n, d, if (!(sigma(d) % n), return (1)); ); return (0); } \\ Michel Marcus, Jan 21 2019

Crossrefs

Cf. A000203, A007691, A081756, A323653.

Sequence in context: A183026 A146005 A325812 * A223346 A109510 A034715

Adjacent sequences: A323649 A323650 A323651 * A323653 A323654 A323655

Keyword

nonn

Author

Jaroslav Krizek, Jan 21 2019

Status

approved