cp's OEIS Frontend

A273787 Least number k such that A001844(k) (sums of two consecutive squares) is the sum of two nonzero squares in exactly n ways.

%I A273787 #19 Feb 16 2018 09:07:02
%S A273787 1,6,21,23,221,78,7278,153,703,1653,6695846,496,670758346,8346,1471,
%T A273787 1081
%N A273787 Least number k such that A001844(k) (sums of two consecutive squares) is the sum of two nonzero squares in exactly n ways.
%C A273787 a(18) = 1978, a(20) = 4596, a(21) = 304153, a(22) = 137903, a(24) = 2628. - _Chai Wah Wu_, Feb 13 2018
%e A273787 a(2) = 6 from 6^2 + 7^2 = 2^2 + 9^2.
%e A273787 a(3) = 21 from 21^2 + 22^2 = 5^2 + 30^2 = 14^2 + 27^2.
%e A273787 a(4) = 23 form 23^2 + 24^2 = 4^2 + 33^2 = 9^2 + 32^2 = 12^2 + 31^2.
%o A273787 (PARI) A025426(n)=my(v=valuation(n, 2), f=factor(n>>v), t=1); for(i=1, #f~, if(f[i, 1]%4>1, if(f[i, 2]%2, return(0)), t*=f[i, 2]+1)); if(t%2, t-(-1)^v, t)/2
%o A273787 a(n)=my(k=1); while(A025426(2*k*(k+1)+1)!=n, k++); k \\ _Charles R Greathouse IV_, Jun 03 2016
%Y A273787 Cf. A001844, A006339, A016032, A025426, A273238.
%K A273787 nonn,more
%O A273787 1,2
%A A273787 _Altug Alkan_, May 30 2016
%E A273787 a(10)-a(14) from _Giovanni Resta_, Jun 03 2016
%E A273787 a(15)-a(16) from _Chai Wah Wu_, Feb 13 2018