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

%I A337806 #17 Sep 28 2020 22:25:33
%S A337806 8,12,16,20,24,27,28,30,32,36,40,44,45,48,52,56,60,63,64,68,70,72,76,
%T A337806 80,81,84,88,90,92,96,99,100,104,105,108,112,116,117,120,124,125,126,
%U A337806 128,132,135,136,140,144,148,150,152,153,154,156,160,164,165,168,171,172,175,176,180,182,184
%N A337806 Numbers that are a divisor of the product of the differences of its consecutive divisors.
%H A337806 Robert Israel, <a href="/A337806/b337806.txt">Table of n, a(n) for n = 1..10000</a>
%e A337806 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.
%e A337806 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.
%e A337806 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.
%e A337806 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.
%p A337806 filter:= proc(n) local R,p;
%p A337806   R:= sort(convert(numtheory:-divisors(n),list));
%p A337806   p:= convert(R[2..-1]-R[1..-2],`*`);
%p A337806   p mod n = 0
%p A337806 end proc:
%p A337806 select(filter, [$2..1000]); # _Robert Israel_, Sep 27 2020
%t A337806 Select[Range[2, 200], Divisible[Times @@ Differences @ Divisors[#], #] &] (* _Amiram Eldar_, Sep 23 2020 *)
%o A337806 (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
%Y A337806 Cf. A193829, A027750. Contains A337877.
%K A337806 nonn
%O A337806 1,1
%A A337806 _Scott R. Shannon_, Sep 23 2020