A352242 -id:A352242 - cp's OEIS frontend

A352244 Positive integers that can be expressed in at least two ways as (x-y)*(x^3-y^3).

57456, 80752, 124852, 229957, 355072, 366471, 630667, 919296, 1193200, 1292032, 1316875, 1371136, 1823472, 1997632, 2036097, 2687607, 3679312, 4251871, 4653936, 5681152, 5821552, 5863536, 6540912, 8905456, 8984196, 10090672, 10113012, 10504375, 10532592, 10789632, 10921456, 14708736

Offset: 1

Michel Marcus, Mar 09 2022, after a suggestion from Vincent Thill

nonn

Integers that appears at least twice in the A352242 triangle.

			57456 is a term since it is A352242(17,5) as well as A352242(26,20).
A term (not necessarily the first) that occurs at least three times in A352242 is 1641000816 = A352242(221,65) = A352242(338,260) = A352242(1955,1943). - _Robert Israel_, May 17 2024

David A. Corneth, Table of n, a(n) for n = 1..12994 (terms <= 10^14)
David A. Corneth, PARI program

Cf. A352242, A352243.

row(n) = vector(n-1, k, (n-k)*(n^3-k^3));
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++;); listsort(list); my(res = List()); for (n=1, #list, if (#select(x->(x==list[n]), list) > 1, if (!vecsearch(Vec(res), list[n]), listput(res, list[n])));); Vec(res);}

PARI
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\\ See PARI link
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A352243 Positive integers of the form (x-y)*(x^3-y^3).

Original entry on oeis.org

7, 19, 37, 52, 61, 91, 112, 127, 169, 189, 196, 217, 271, 304, 331, 351, 397, 436, 469, 496, 547, 567, 592, 631, 721, 772, 817, 832, 837, 919, 976, 1027, 1075, 1141, 1161, 1204, 1261, 1264, 1387, 1456, 1519, 1539, 1657, 1675, 1732, 1792, 1801, 1951, 1971, 2032, 2052

Offset: 1

Michel Marcus, Mar 09 2022

nonn

Integers that are in the A352242 triangle.

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

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

Cf. A352242, A352244.

N:= 10^4: # for terms <= N
S:= {}:
for y from 1 while 3*y^2 + 3*y + 1 <= N do
  for x from y+1 do
    v:= (x-y)*(x^3-y^3);
    if v > N then break fi;
    S:= S union {v};
od; od:
sort(convert(S,list)); # Robert Israel, May 16 2024

row(n) = vector(n-1, k, (n-k)*(n^3-k^3));
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));}

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A352244 Positive integers that can be expressed in at least two ways as (x-y)*(x^3-y^3).

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A352243 Positive integers of the form (x-y)*(x^3-y^3).

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