A352243 - OEIS

%I #11 May 17 2024 01:28:37

%S 7,19,37,52,61,91,112,127,169,189,196,217,271,304,331,351,397,436,469,

%T 496,547,567,592,631,721,772,817,832,837,919,976,1027,1075,1141,1161,

%U 1204,1261,1264,1387,1456,1519,1539,1657,1675,1732,1792,1801,1951,1971,2032,2052

%N Positive integers of the form (x-y)*(x^3-y^3).

%C Integers that are in the A352242 triangle.

%H Robert Israel, <a href="/A352243/b352243.txt">Table of n, a(n) for n = 1..10000</a>

%e 7, 19, 37, 52 and 61 are respectively A352242(1,1), A352242(2,2), A352242(3,3), A352242(2,1) and A352242(4,4).

%p N:= 10^4: # for terms <= N

%p S:= {}:

%p for y from 1 while 3*y^2 + 3*y + 1 <= N do

%p   for x from y+1 do

%p     v:= (x-y)*(x^3-y^3);

%p     if v > N then break fi;

%p     S:= S union {v};

%p od; od:

%p sort(convert(S,list)); # _Robert Israel_, May 16 2024

%o (PARI) row(n) = vector(n-1, k, (n-k)*(n^3-k^3));

%o lista(nn) = {my(list = List(), n=2); while (3*n*(n-1)+1 <= nn, my(rown = row(n)); for (k=1, #rown, if (rown[k] <= nn, listput(list, rown[k]))); n++;); Set(Vec(list));}

%Y Cf. A352242, A352244.

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 09 2022