A110346 Largest multiple of n in n + (n-1) +(n-2) + ... (n-k).

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

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(2n-1) = n(2n-1).

a(2^n) = 2^n. - Ivan Neretin, May 17 2015

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

Maple

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:
map(F, [$1..100]); # Robert Israel, May 17 2015

Mathematica

Table[Max[Select[n (n + 1)/2 - # (# - 1)/2 & /@ Range[n], Divisible[#, n] &]], {n, 55}] (* Ivan Neretin, May 17 2015 *)

Prog

;; PLT DrScheme (Zucker)
(define (A110346 n)
(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.

Crossrefs

Sequence in context: A069914 A200746 A130190 * A095754 A226718 A181159

Adjacent sequences: A110343 A110344 A110345 * A110347 A110348 A110349

Keyword

easy,nonn

Author

Amarnath Murthy, Jul 20 2005

Extensions

More terms from Joshua Zucker, May 09 2006

Status

approved