A178919 Smallest of three consecutive integers divisible respectively by three consecutive squares greater than 1.

2223, 5823, 9423, 13023, 16623, 20223, 23823, 27423, 31023, 32975, 34623, 38223, 41823, 45423, 49023, 52623, 56223, 59823, 63423, 67023, 70623, 74223, 77075, 77823, 81423, 85023, 88623, 92223, 95823, 99423, 103023, 106623, 110223

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

5823 is a term as 5823, 5824 and 5825 are divisible by 9, 16 and 25 respectively.

Maple

with(numtheory):for n from 1 to 200000 do: k:=0:q:=floor(sqrt(n)):for m from
  2 to q do: p1:=m^2:p2:=(m+1)^2:p3:=(m+2)^2:if irem(n, p1)=0 and irem(n+1, p2)=0
  and irem(n+2, p3)=0 and k=0 then k:=1:printf(`%d, `, n):else fi:od:od:

Mathematica

f[p_, e_] := p^Floor[e/2]; maxsq[n_] := Times@@ (f @@@ FactorInteger[n]); aQ[n_] := (s = maxsq[n]) > 1 && AnyTrue[Rest @ Divisors[s], Divisible[n+1, (#+1)^2] && Divisible[n+2, (#+2)^2] &]; Select[Range[50000], aQ] (* Amiram Eldar, Sep 09 2019 *)

Prog

(Sage) is_A178919 = lambda n: any(all(((k+x)**2).divides(n+x) for x in range(3)) for k in divisors(n) if k > 1) # D. S. McNeil, Dec 29 2010

Crossrefs

Cf. A178918.

Sequence in context: A043500 A118116 A053395 * A205225 A236496 A208181

Adjacent sequences: A178916 A178917 A178918 * A178920 A178921 A178922

Keyword

nonn

Author

Michel Lagneau, Dec 29 2010

Status

approved