A083482 Square root of smallest square of the type n(n+1)*k.

2, 6, 6, 10, 30, 42, 28, 12, 30, 110, 66, 78, 182, 210, 60, 68, 102, 114, 190, 210, 462, 506, 276, 60, 130, 234, 126, 406, 870, 930, 248, 264, 1122, 1190, 210, 222, 1406, 1482, 780, 820, 1722, 1806, 946, 330, 690, 2162, 564, 84, 70, 510, 1326, 1378, 954, 990

Offset: 1

Author

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

Keywords

• nonn

Comments

Squares pertaining to A083481.

a(n) == (p*q*r... ) where p,q,r are prime factors of n(n+1).

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A083481.

Programs

Mathematica

Table[Times @@ ((a = Transpose[FactorInteger[n (n + 1)]])[[1]]^Quotient[a[[2]] + 1, 2]), {n, 54}] (* Ivan Neretin, May 20 2015 *)

PARI

a(n)=sqrt(n*(n+1)*core(n*(n+1)))

Python

from math import prod
from sympy import factorint
def A083482(n): return n*(n+1)//prod(p**(q>>1) for p, q in factorint(n*(n+1)).items()) # Chai Wah Wu, Mar 20 2023

Formula

a(n) = sqrt(A002378(n)*A083481(n)) = sqrt(A002378(n)*A007913(A002378(n))). a(n) = A019554(A002378(n)). - David Wasserman, Nov 16 2004

Extensions

More terms from Benoit Cloitre, May 04 2003

More terms from David Wasserman, Nov 16 2004