A396825 Positive integers that don't occur in A397366.

1, 4, 9, 12, 16, 25, 28, 33, 36, 49, 60, 64, 81, 96, 100, 121, 124, 144, 169, 193, 196, 225, 228, 256, 288, 289, 324, 336, 361, 385, 400, 420, 441, 484, 529, 576, 625, 676, 708, 729, 768, 784, 841, 900, 961, 1024, 1089, 1152, 1156, 1216, 1225, 1296, 1344, 1369

Offset

1,2

Comments

The sequence complements the set of values in the linked table. The sequence contains all squares >= 1.

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 1..160

Carl Pomerance and Andreas Weingartner, Exceptions to the Erdős-Straus-Schinzel conjecture, arXiv:2511.16817 [math.NT], 2026.

Alan Swett, Alternative Calculation of S(n), 1999.

Alan Swett, Table of Values of S(n), 1999.

Formula

a(n) = {0, 1, 4, 9} (mod 12).

Prog

(PARI) first(nn, m=(nn\2+12)^3)= my(u=Map()); for(n=1, m, foreach((divisors(n^2)*-4)%(4*n-1), k, mapisdefined(u, k) || mapput(~u, k, 0))); [i|i<-[1..vecmax(Vec(u))], !mapisdefined(u, i)][1..nn]; \\ m is heuristic

Crossrefs

Cf. A139665, A292581, A397366.

Sequence in context: A034018 A386627 A320924 * A357976 A330879 A357636

Adjacent sequences: A396822 A396823 A396824 * A396826 A396827 A396828

Keyword

nonn,new

Author

Ruud H.G. van Tol, Jun 07 2026

Status

approved