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A242806 Integers k such that each of k, k+1, k+2, k+4, k+5, k+6 is the squarefree product of four primes.

%I A242806 #30 Jul 12 2025 16:12:38
%S A242806 9743613,9780589,22669381,23209809,23395137,26143197,28042877,
%T A242806 38110029,43335609,45127905,45559613,47163489,47944865,48030229,
%U A242806 48611913,48762829,50015301,50600341,50742501,51256541,52691613
%N A242806 Integers k such that each of k, k+1, k+2, k+4, k+5, k+6 is the squarefree product of four primes.
%C A242806 This is a higher analog to A242804 and A242805.
%e A242806 9743613=3*11*503*587, 9743614=2*59*71*1163, 9743615= 5*7*167*1667, 9743617=13*37*47*431, 9743618=2*17*19*15083, 9743619=3*83*109*359.
%t A242806 sfp4Q[n_]:=With[{c=n+{0,1,2,4,5,6}},Union[PrimeNu[c]]=={4}&&AllTrue[c,SquareFreeQ]]; Select[Range[52700000],sfp4Q] (* _Harvey P. Dale_, Jul 11 2025 *)
%o A242806 (PARI)
%o A242806 { default(primelimit, 1000M); i=0; j=0; k=0; l=0; m=0; loc=0; lb=2; ub=9*10^9; o=4; for(n=lb, ub, if(issquarefree(n)&&(o==omega(n)), loc=loc+1; if(1==loc, i=n; ); if(2==loc, if(i+1==n, j=n; ); if(i+1<n, loc=1; i=n; ); ); if(3==loc, if(j+1==n, k=n; ); if(j+1<n, loc=1; i=n; ); ); if(4==loc, if(k+2==n, l=n; ); if(k+2<n, loc=1; i=n; ); ); if(5==loc, if(l+1==n, m=n; ); if(l+1<n, loc=1; i=n; ); ); if(6==loc, if(m+1==n, print1(i,","); loc=0; ); if(m+1<n, loc=1; i=n; ); ); ); ); }
%Y A242806 Cf. A242793 and A242804 (two primes), A242805 (three primes), A242829 (five primes).
%K A242806 nonn,more
%O A242806 1,1
%A A242806 _Daniel Constantin Mayer_, May 23 2014