A078936 Smallest divisor of n*(n+1)/2 that is >= sqrt(n*(n+1)/2).

1, 3, 3, 5, 5, 7, 7, 6, 9, 11, 11, 13, 13, 15, 12, 17, 17, 19, 19, 15, 21, 23, 23, 20, 25, 27, 21, 29, 29, 31, 31, 24, 33, 35, 30, 37, 37, 39, 30, 41, 41, 43, 43, 33, 45, 47, 47, 42, 35, 51, 39, 53, 53, 45, 44, 42, 57, 59, 59, 61, 61, 63, 48, 52, 55, 67, 67, 51, 69, 71, 71, 73

Offset

1,2

Comments

Greater side of integral rectangle with area n*(n+1)/2 having minimal semiperimeter.

a(n) <= n+1, with equality if n is in A100484. - Robert Israel, Apr 16 2025

Links

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

Formula

a(n) = A033677(A000217(n)).

a(n) = A078934(n) - A078935(n)

a(n)*A078935(n) = A000217(n).

Maple

f:= proc(x) min(select(t -> t^2 >= x, numtheory:-divisors(x))) end proc:
map(f, [seq(n*(n+1)/2, n=1..100)]); # Robert Israel, Apr 16 2025

Mathematica

a[n_] := Select[Divisors[n*(n+1)/2], # >= Sqrt[n*(n+1)/2] &, 1][[1]]; Array[a, 100] (* Amiram Eldar, Aug 03 2024 *)

Crossrefs

Cf. A000217, A033677, A078934, A078935, A100484.

Sequence in context: A069902 A335568 A085779 * A293702 A061794 A088524

Adjacent sequences: A078933 A078934 A078935 * A078937 A078938 A078939

Keyword

nonn

Author

Reinhard Zumkeller, Dec 17 2002

Status

approved