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%I #39 Nov 10 2023 17:27:42
%S 17,241,242,1249,4049,4799,17297,120049,206081,281249,388961,470447,
%T 538721,1462049,1566449,1808801,1916881,3302449,3302450,3693761,
%U 3959297,5385761,5664976,6118001,6986321,9305297,10479041,14268481,16831601,20110481,22997761,27661922,28140001
%N Numbers m such that each of the four consecutive integers m, m+1, m+2, m+3 has squarefree rank 1.
%C A162642(k) is the squarefree rank of k.
%C Numbers that are the first of four consecutive terms of A228056 form a subsequence: 242, 3302450, 22997761, 27661922, 28140001, 64866050, ... consisting of those numbers m in this sequence such that m, m+1, m+2, and m+3 are all composite. - _Charles R Greathouse IV_, Sep 30 2021
%C One of for positive integer m, m+1, m+2, m+3 is of the form 4*k + 2 = 2*(2*k + 1). As 2 has an odd exponent the exponents in the prime factorization and 2*k + 1 is odd, the number of odd exponents in the prime factorization of 2*k + 1 must be 0 i.e., 2*k + 1 is a perfect square and so one of m, m+1, m+2, m+3 is of the form 2*t^2 where t is an odd square. - _David A. Corneth_, Nov 09 2023
%H David A. Corneth, <a href="/A290340/b290340.txt">Table of n, a(n) for n = 1..10000</a> (first 79 terms from Jason Kimberley, a(n) for n = 80..347 from Charles R Greathouse IV)
%H David A. Corneth, <a href="/A290340/a290340.gp.txt">PARI program</a>
%e m = 17 is in the sequence as the number of odd prime exponents of each of the numbers m = 17 through m + 3 = 20 is 1. - _David A. Corneth_, Nov 06 2023
%o (Magma)
%o A162642:=func<n|&+[Integers()|pe[2]mod 2:pe in Factorisation(n)]>;
%o c:=func<a|[n:n in a|n+1 in a]>;
%o c(c(c([n:n in[1..10^6]|A162642(n)eq 1])));
%o (PARI) list(lim)=my(u=vectorsmall(4),v=List(),s,i); forfactored(n=2,lim\1+3, if(i++>4,i=1); s-=u[i]; s+=u[i]=(vecsum(n[2][,2]%2)==1); if(s==4, listput(v,n[1]-3))); Vec(v); \\ _Charles R Greathouse IV_, Sep 30 2021
%o (PARI) \\ See PARI link
%Y Cf. A162642, A229125, A277225, A228056.
%K nonn
%O 1,1
%A _Jason Kimberley_, Jul 27 2017
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