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Square root of smallest square of the type n(n+1)*k.
3

%I #16 Mar 20 2023 10:10:47

%S 2,6,6,10,30,42,28,12,30,110,66,78,182,210,60,68,102,114,190,210,462,

%T 506,276,60,130,234,126,406,870,930,248,264,1122,1190,210,222,1406,

%U 1482,780,820,1722,1806,946,330,690,2162,564,84,70,510,1326,1378,954,990

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

%C Squares pertaining to A083481.

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

%H Ivan Neretin, <a href="/A083482/b083482.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = sqrt(A002378(n)*A083481(n)) = sqrt(A002378(n)*A007913(A002378(n))). a(n) = A019554(A002378(n)). - _David Wasserman_, Nov 16 2004

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

%o (PARI) a(n)=sqrt(n*(n+1)*core(n*(n+1)))

%o (Python)

%o from math import prod

%o from sympy import factorint

%o 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

%Y Cf. A083481.

%K nonn

%O 1,1

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003

%E More terms from _Benoit Cloitre_, May 04 2003

%E More terms from _David Wasserman_, Nov 16 2004