cp's OEIS Frontend

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

%I A323652 #20 Apr 07 2025 14:57:07
%S A323652 1,6,12,28,56,120,360,496,672,992,2016,8128,16256,30240,32760,60480,
%T A323652 65520,120960,131040,523776,1571328,2178540,4357080,8714160,23569920,
%U A323652 33550336,45532800,47139840,67100672,91065600,94279680,142990848,182131200,285981696
%N A323652 Numbers m having at least one divisor d such that m divides sigma(d).
%C A323652 Generalization of multiperfect numbers (A007691).
%C A323652 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.
%C A323652 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?
%C A323652 Supersequence of A081756.
%e A323652 12 is a term because 6 divides 12 and simultaneously 12 divides sigma(6) = 12.
%t A323652 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 *)
%o A323652 (Magma) [n: n in [1..10000] | #[d: d in Divisors(n) | SumOfDivisors(d) mod n eq 0] gt 0];
%o A323652 (PARI) isok(n) = {fordiv(n, d, if (!(sigma(d) % n), return (1));); return (0);} \\ _Michel Marcus_, Jan 21 2019
%Y A323652 Cf. A000203, A007691, A081756, A323653.
%K A323652 nonn
%O A323652 1,2
%A A323652 _Jaroslav Krizek_, Jan 21 2019