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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A193829, A027750. Contains A337877.

Sequence in context: A253296 A081925 A049199 * A377316 A192544 A302139

Adjacent sequences: A337803 A337804 A337805 * A337807 A337808 A337809

Keyword

nonn

Author

Scott R. Shannon, Sep 23 2020

Status

approved