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

Author

Jaroslav Krizek, Jan 21 2019

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A000203, A007691, A081756, A323653.

Programs

Magma

[n: n in [1..10000] | #[d: d in Divisors(n) | SumOfDivisors(d) mod n eq 0] gt 0];

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 *)

PARI

isok(n) = {fordiv(n, d, if (!(sigma(d) % n), return (1));); return (0);} \\ Michel Marcus, Jan 21 2019