A389554 a(n) = number of triples (a,b,c) such that a!*b!*c! is a perfect square, with 1 <= a < b < c = A388851(n).

1, 2, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 1, 4, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Mathematica

Table[Module[{t = 0}, If[CompositeQ[c], Do[If[IntegerQ[Sqrt[a!*c!/b!]], t++], {b, NextPrime[c, -1], c-1}, {a, b-1}]]; If[t > 0, t, Nothing]], {c, 300}]

Crossrefs

Row lengths of A389553, divided by 3.

Cf. A388851, A389555.

Sequence in context: A308069 A161895 A048138 * A165022 A030338 A231148

Adjacent sequences: A389551 A389552 A389553 * A389555 A389556 A389557

Keyword

nonn

Author

Paolo Xausa, Oct 09 2025

Status

approved