A178918 - OEIS

A178918

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

%I #14 Sep 09 2019 11:56:57

%S 8,44,63,80,116,152,188,207,224,260,296,332,351,368,404,440,476,495,

%T 512,548,575,584,620,624,639,656,692,728,764,783,800,836,872,908,927,

%U 944,980,1016,1024,1052,1071,1088,1124,1160,1196,1215,1224,1232

%N Smallest of two consecutive integers divisible respectively by two consecutive squares greater than 1.

%H Amiram Eldar, <a href="/A178918/b178918.txt">Table of n, a(n) for n = 1..10000</a>

%e 1791 is a term as 1791 and 1792 are divisible by 9 and 16 respectively.

%p with(numtheory):for n from 1 to 2000 do: k:=0:q:=floor(sqrt(n)):for m from

%p 2 to q do: p1:=m^2:p2:=(m+1)^2:if irem(n,p1)=0 and irem(n+1,p2)=0 and k=0 then

%p k:=1:printf(`%d, `,n):else fi:od:od:

%t 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] &]; Select[Range[1232], aQ] (* _Amiram Eldar_, Sep 09 2019 *)

%o (Sage) is_A178918 = lambda n: any(all(((k+x)**2).divides(n+x) for x in range(2)) for k in divisors(n) if k > 1) # _D. S. McNeil_, Dec 29 2010

%Y Cf. A178919.

%K nonn

%O 1,1

%A _Michel Lagneau_, Dec 29 2010