A390004 a(n) = number of quadruples (a,b,c,d) such that a!*b!*c!*d! is a perfect square, with 1 <= a < b < c < d = A387184(n).

2, 1, 2, 5, 2, 3, 4, 6, 3, 4, 6, 4, 3, 6, 1, 4, 7, 3, 4, 1, 2, 4, 8, 1, 2, 3, 3, 1, 6, 4, 9, 15, 3, 2, 6, 4, 6, 1, 3, 1, 3, 9, 8, 2, 3, 7, 6, 2, 1, 4, 6, 13, 1, 4, 1, 1, 4, 3, 2, 1, 7, 8, 4, 12, 2, 2, 7, 7, 2, 5, 1, 3, 5, 14, 1, 1, 8, 9, 9, 2, 1, 4, 5, 2, 6

Offset

1,1

Links

Table of n, a(n) for n=1..85.

Mathematica

Table[Module[{t = 0}, If[CompositeQ[d], Do[If[IntegerQ[Sqrt[d!/c!*b!/a!]], t++], {c, NextPrime[d, -1], d-1}, {b, 2, c-1}, {a, b-1}]]; If[t > 0, t, Nothing]], {d, 100}]

Prog

(PARI) a390004(m=150) = my(v=vector(m)); for(a=1, m-3, for(b=a+1, m-2, for(c=b+1, m-1, for(d=c+1, nextprime(c+1), my(P=a!*b!*c!*d!); if(issquare(P), v[d]++))))); select(x -> x>0, v) \\ Hugo Pfoertner, Oct 22 2025

Crossrefs

Row lengths of A390003, divided by 4.

Cf. A316341, A387184, A389554, A390005.

Sequence in context: A109631 A361399 A337222 * A095149 A218579 A329198

Adjacent sequences: A390001 A390002 A390003 * A390005 A390006 A390007

Keyword

nonn

Author

Paolo Xausa, Oct 21 2025

Status

approved