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A013654 Each term of the period of continued fraction for sqrt(n) divides n. 1
2, 8, 12, 24, 30, 48, 56, 80, 90, 120, 132, 168, 182, 224, 240, 288, 306, 360, 380, 440, 462, 528, 552, 624, 650, 728, 756, 840, 870, 960, 992, 1088, 1122, 1224, 1260, 1368, 1406, 1520, 1560, 1680, 1722, 1848, 1892, 2024, 2070, 2208, 2256, 2400, 2450, 2600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = n(n+1) if n is odd and n(n+2) if n is even. - Wesley Ivan Hurt, Nov 19 2013

REFERENCES

H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th edition, 1999, Table 1.

Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 426 (but beware of errors!).

LINKS

Table of n, a(n) for n=1..50.

FORMULA

a(2n)= 2*(n+1)*(2n), a(2n+1)= 2*(n+1)*(2n+1). - Frank Ellermann, Feb 22 2002

G.f.:(-2-6*x)/((x+1)^2*(x-1)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

a(n) = n * (n + 1 + (1+(-1)^n)/2). - Wesley Ivan Hurt, Nov 19 2013

MAPLE

A013654:=n->n*(n+1+(1+(-1)^n)/2); seq(A013654(n), n=1..100); # Wesley Ivan Hurt, Nov 19 2013

MATHEMATICA

Table[n(n+1+(1+(-1)^n)/2), {n, 100}] (* Wesley Ivan Hurt, Nov 19 2013 *)

CROSSREFS

Sequence in context: A063622 A162152 A280252 * A277804 A108978 A269968

Adjacent sequences:  A013651 A013652 A013653 * A013655 A013656 A013657

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)