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A009005
All natural numbers except 1, 2 and 4.
7
3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77
OFFSET
1,1
COMMENTS
Short legs of Pythagorean triangles.
Also the natural numbers n such that there is an open knight's tour of the 4 X n chessboard. - Sharon Sela (sharonsela(AT)hotmail.com), Jan 02 2002
Also perimeters of integral triangles; equivalently, numbers n = a + b + c, where a + b > c, a + c > b, b + c > a, and a, b, c are integers (necessarily a, b, c, and n are positive). - Rick L. Shepherd, Aug 04 2013
Along with 0, possible scores in rugby union, where points can be scored with a penalty goal or drop goal (3 points), try (5 points) and converted try (7 points). - Charles R Greathouse IV, Sep 10 2016
Also the positive integers n such that floor(t(n+2)/(t(n+2) - sigma(n+2))) = 1, where t(n) = n*(n+1)/2 = A000217(n) and sigma(n) = A000203(n) (see A242963). - Lorenzo Sauras Altuzarra, Jan 29 2020
FORMULA
O.g.f.: x(3-x-x^2)/(1-x)^2. a(n)=A009056(n), n>1. - R. J. Mathar, May 26 2008
MATHEMATICA
Join[{3}, Range[5, 100]] (* Paolo Xausa, Sep 13 2024 *)
PROG
(PARI) a(n)=n+4-(n==1) \\ Charles R Greathouse IV, Sep 02 2011
CROSSREFS
Cf. A000203 (sigma function), A000217 (triangular numbers), A242963.
Sequence in context: A009004 A005527 A285173 * A362018 A138884 A008521
KEYWORD
nonn,easy
STATUS
approved