cp's OEIS Frontend

A070284 Smallest of 4 consecutive numbers each divisible by a square.

%I A070284 #23 Jan 09 2025 02:57:07
%S A070284 242,844,845,1680,1681,2888,2889,3174,3624,3625,3750,5046,5047,8475,
%T A070284 8523,8954,10050,10827,10924,10925,11322,13374,14748,14749,15775,
%U A070284 15848,15849,16575,17404,17405,19647,19940,19941,20574,21462
%N A070284 Smallest of 4 consecutive numbers each divisible by a square.
%C A070284 This sequence has positive density in N; the density is around 0.0025.
%C A070284 The sequence includes an infinite family of arithmetic progressions. Such AP's can be constructed to each term, with large differences [like e.g. square of primorials, A061742]. It is necessary to solve suitable systems of linear Diophantine equations. E.g.: subsequences of quadruples of terms = {44100k+29349, 44100k+29350, 44100k+29351, 44100k+29352} = {9(4900k+3261), 25(1764k+1174), 49(900k+599), 4(11025k+7338)}; starting terms in this sequence = {29349, 73449, 117549, ...}; difference = A002110(4)^2 = 210^2. - _Labos Elemer_, Nov 25 2002
%H A070284 Charles R Greathouse IV, <a href="/A070284/b070284.txt">Table of n, a(n) for n = 1..10000</a>
%F A070284 A070284 = { A070258[k] | A070258[k+1] = A070258[k]+1 }. - _M. F. Hasler_, Feb 01 2016
%t A070284 f[n_] := Union[Transpose[FactorInteger[n]][[2]]][[ -1]]; a = 0; b = 1; c = 0; Do[d = f[n]; If[a > 1 && b > 1 && c > 1 && d > 1, Print[n - 3]]; a = b; b = c; c = d, {n, 4, 10^6}]
%t A070284 Flatten[Position[Partition[SquareFreeQ/@Range[60000],4,1],_?(Union[#] == {False}&),{1},Heads->False]] (* _Harvey P. Dale_, May 24 2014 *)
%o A070284 (PARI) is(n)=for(i=n,n+3, if(!issquarefree(n), return(0))); 1 \\ _Charles R Greathouse IV_, Sep 14 2015
%Y A070284 Cf. A070258, A068781, A045882, A049535, A077647, A078143.
%K A070284 nonn
%O A070284 1,1
%A A070284 Sharon Sela (sharonsela(AT)hotmail.com), May 09 2002
%E A070284 More terms from _Robert G. Wilson v_, May 09 2002
%E A070284 b-file from _Charles R Greathouse IV_, Jul 23 2010