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

Author

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

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A002378, A007913, A083482.

Programs

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 *)

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

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

Extensions

More terms from Benoit Cloitre, May 04 2003