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A110346
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Largest multiple of n in n + (n-1) +(n-2) + ... (n-k).
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1
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1, 2, 6, 4, 15, 18, 28, 8, 45, 40, 66, 72, 91, 84, 120, 16, 153, 126, 190, 200, 231, 198, 276, 264, 325, 260, 378, 196, 435, 450, 496, 32, 561, 442, 630, 288, 703, 570, 780, 520, 861, 882, 946, 924, 1035, 828, 1128, 1056, 1225, 950, 1326, 1300, 1431, 1134, 1540
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OFFSET
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1,2
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LINKS
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FORMULA
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a(2n-1) = n(2n-1).
a(n) = n*k + n - (k^2+k)/2 where k is the greatest integer <= n with k*(k+1) divisible by 2*n. k = n iff n is odd. - Robert Israel, May 17 2015
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MAPLE
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F:= proc(n) local k, R;
k:= max(map(t -> `if`(t[1]<= n, t[1], NULL), Roots(k*(k+1)) mod (2*n)));
n*k + n - (k^2+k)/2;
end proc:
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MATHEMATICA
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Table[Max[Select[n (n + 1)/2 - # (# - 1)/2 & /@ Range[n], Divisible[#, n] &]], {n, 55}] (* Ivan Neretin, May 17 2015 *)
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PROG
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;; PLT DrScheme (Zucker)
(apply max (filter (lambda (x) (= 0 (remainder x n)))
(build-list n (lambda (k) (apply + (build-list (add1 k) (lambda (j) (- n j)))))))))
;; yes, it would be faster to use n(n+1)/2 - k(k+1)/2 instead of summing.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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