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.
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 21 2019
STATUS
approved