A337806 Numbers that are a divisor of the product of the differences of its consecutive divisors.

8, 12, 16, 20, 24, 27, 28, 30, 32, 36, 40, 44, 45, 48, 52, 56, 60, 63, 64, 68, 70, 72, 76, 80, 81, 84, 88, 90, 92, 96, 99, 100, 104, 105, 108, 112, 116, 117, 120, 124, 125, 126, 128, 132, 135, 136, 140, 144, 148, 150, 152, 153, 154, 156, 160, 164, 165, 168, 171, 172, 175, 176, 180, 182, 184

Offset: 1

Author

Scott R. Shannon, Sep 23 2020

Keywords

• nonn

Examples

			8 is a term as the divisors of 8 are 1,2,4,8, the differences of which are 1,2,4, and 1*2*4 = 8 which is a multiple of 8.
20 is a term as the divisors of 20 are 1,2,4,5,10,20, the differences of which are 1,2,1,5,10, and 1*2*1*5*10 = 100 which is a multiple of 20.
27 is a term as the divisors of 27 are 1,3,9,27, the differences of which are 2,6,18, and 2*6*18 = 216 which is a multiple of 27.
99 is a term as the divisors of 99 are 1,3,9,11,33,99, the difference of which are 2,6,2,22,66, and 2*6*2*22*66 = 34848 which is a multiple of 99.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A193829, A027750. Contains A337877.

Programs

Maple

filter:= proc(n) local R,p;
  R:= sort(convert(numtheory:-divisors(n),list));
  p:= convert(R[2..-1]-R[1..-2],`*`);
  p mod n = 0
end proc:
select(filter, [$2..1000]); # Robert Israel, Sep 27 2020

Mathematica

Select[Range[2, 200], Divisible[Times @@ Differences @ Divisors[#], #] &] (* Amiram Eldar, Sep 23 2020 *)

PARI

isok(k) = my(d=divisors(k)); (#d > 1) && (vecprod(vector(#d-1, k, d[k+1]-d[k])) % k) == 0; \\ Michel Marcus, Sep 23 2020