A067572 Numbers n such that determinant[{{n, sigma(n)}, {n+1, sigma(n+1)}}] is a perfect square.

1, 15, 62, 1061, 16049, 163863, 288099, 1416729, 2083059, 13348207, 30204871, 35154349, 59852792, 63224809, 283280355, 464690354, 484273317, 546188411, 950441582, 1282519339, 1395158907, 1406767949, 1438132761, 2530805413, 3442427162, 4774940354, 9019693953

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..27.

Example

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

Mathematica

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

Crossrefs

Cf. A000203.

Sequence in context: A240711 A212055 A219296 * A066584 A065915 A062965

Adjacent sequences: A067569 A067570 A067571 * A067573 A067574 A067575

Keyword

nonn

Author

Joseph L. Pe, Jan 30 2002

Extensions

a(8)-a(27) from Amiram Eldar, Aug 14 2019

Status

approved