A277225 -id:A277225 - cp's OEIS frontend

A290340 Numbers m such that each of the four consecutive integers m, m+1, m+2, m+3 has squarefree rank 1.

17, 241, 242, 1249, 4049, 4799, 17297, 120049, 206081, 281249, 388961, 470447, 538721, 1462049, 1566449, 1808801, 1916881, 3302449, 3302450, 3693761, 3959297, 5385761, 5664976, 6118001, 6986321, 9305297, 10479041, 14268481, 16831601, 20110481, 22997761, 27661922, 28140001

Offset: 1

Jason Kimberley, Jul 27 2017

nonn

A162642(k) is the squarefree rank of k.
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
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

			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

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 79 terms from Jason Kimberley, a(n) for n = 80..347 from Charles R Greathouse IV)
David A. Corneth, PARI program

Cf. A162642, A229125, A277225, A228056.

A162642:=func;
c:=func;
c(c(c([n:n in[1..10^6]|A162642(n)eq 1])));

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

PARI
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\\ See PARI link
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cp's OEIS Frontend

A290340 Numbers m such that each of the four consecutive integers m, m+1, m+2, m+3 has squarefree rank 1.

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