A083481 Squarefree part of the n-th oblong number.

2, 6, 3, 5, 30, 42, 14, 2, 10, 110, 33, 39, 182, 210, 15, 17, 34, 38, 95, 105, 462, 506, 138, 6, 26, 78, 21, 203, 870, 930, 62, 66, 1122, 1190, 35, 37, 1406, 1482, 390, 410, 1722, 1806, 473, 55, 230, 2162, 141, 3, 2, 102, 663, 689, 318, 330, 770, 798, 3306, 3422, 885

Offset

1,1

Comments

Smallest k such that n*(n+1)*k is a perfect square.

k = p*q*r... is a squarefree number where p,q,r are those prime factors of n(n+1) which have odd index.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

John M. Campbell, An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences, arXiv preprint arXiv:1105.3399 [math.GM], 2011.

Formula

a(n) = A007913(n*(n+1)). - R. J. Mathar, Nov 02 2011

a(n) = A007913(n) * A007913(n+1). - Amiram Eldar, Jul 10 2024

Maple

A083481 := proc(n)
    A007913(n)*A007913(n+1) ;
end proc:
seq( A083481(n), n=1..40) ; # R. J. Mathar, Mar 15 2023

Mathematica

sk[n_]:=Module[{k=1}, While[!IntegerQ[Sqrt[n*k]], k++]; k]; sk/@Table[n(n+1), {n, 60}] (* Harvey P. Dale, Mar 28 2013 *)

Prog

(PARI) a(n)=core(n*(n+1))
(Python)
from sympy.ntheory.factor_ import core
def A083481(n): return core(n*(n+1)) # Chai Wah Wu, Mar 20 2023

Crossrefs

Cf. A002378, A007913, A083482.

Sequence in context: A323335 A338444 A139384 * A177209 A274439 A280342

Adjacent sequences: A083478 A083479 A083480 * A083482 A083483 A083484

Keyword

nonn,easy

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003

Extensions

More terms from Benoit Cloitre, May 04 2003

Status

approved