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A067572
Numbers n such that determinant[{{n, sigma(n)}, {n+1, sigma(n+1)}}] is a perfect square.
1
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.
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
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Jan 30 2002
EXTENSIONS
a(8)-a(27) from Amiram Eldar, Aug 14 2019
STATUS
approved