A081468 a(n) is the smallest multiple of n of the type k*n + k*(k+1)/2, i.e., the smallest sum (n+1) to (n+k) which is divisible by n.

2, 12, 9, 56, 30, 24, 63, 240, 108, 50, 165, 132, 234, 126, 90, 992, 408, 180, 513, 420, 147, 308, 759, 480, 900, 390, 1053, 224, 1218, 570, 1395, 4032, 429, 680, 595, 324, 1998, 912, 546, 720, 2460, 1050, 2709, 1936, 450, 1334, 3243, 2064, 3528, 1500, 1020

Offset

1,1

Comments

From Robert Israel, Jun 26 2018: (Start)

a(n) = 3*n*(n-1)/2 if n is an odd prime power.

a(2^k) = 4^(k+1) - 2^(k+1). (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4) = 5 + 6 + 7 + 8 + 9 + 10 + 11 = 56; A081467(4) = 11.

Maple

f:= proc(n) local k;
  k:= min(map(t ->rhs(op(t)), {msolve(k*(k+1), 2*n)}) minus {0});
  k*n+k*(k+1)/2
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Jun 26 2018

Mathematica

a[n_] := For[k = 1, True, k++, If[Divisible[m = k n + k(k+1)/2, n], Return[m] ] ]; Array[a, 100] (* Jean-François Alcover, Mar 25 2019 *)

Prog

(PARI) a(n) = {my(k = 1); while((s=k*n + k*(k+1)/2) % n, k++); s; } \\ Michel Marcus, Jul 29 2017

Crossrefs

Cf. A081467, A081469, A081470, A081471, A081472.

Sequence in context: A002209 A100654 A166544 * A216349 A280015 A343645

Adjacent sequences: A081465 A081466 A081467 * A081469 A081470 A081471

Keyword

nonn,look

Author

Amarnath Murthy, Mar 23 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

Status

approved