A067572 - OEIS

%I #9 Aug 14 2019 08:25:26

%S 1,15,62,1061,16049,163863,288099,1416729,2083059,13348207,30204871,

%T 35154349,59852792,63224809,283280355,464690354,484273317,546188411,

%U 950441582,1282519339,1395158907,1406767949,1438132761,2530805413,3442427162,4774940354,9019693953

%N Numbers n such that determinant[{{n, sigma(n)}, {n+1, sigma(n+1)}}] is a perfect square.

%C If n is a term of the sequence, then the parallelogram formed by the vectors {n, sigma(n)}, {n+1, sigma(n+1)} has the same area as that of an integral square.

%e Det[{{15, sigma(15)},{16, sigma(16)}}] = Det[{{15,24},{16,31}}] = 9^2, so 15 is a term of the sequence.

%t f[n_] := Det[{{n, DivisorSigma[1, n]}, {n + 1, DivisorSigma[1, n + 1]}}]; Do[If[f[n] == 0, Print[n]], {n, 1, 10^6}]

%Y Cf. A000203.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Jan 30 2002

%E a(8)-a(27) from _Amiram Eldar_, Aug 14 2019