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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A245281

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

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Last modified August 7 22:44 EDT 2020. Contains 336279 sequences. (Running on oeis4.)