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

%I A083482 #16 Mar 20 2023 10:10:47
%S A083482 2,6,6,10,30,42,28,12,30,110,66,78,182,210,60,68,102,114,190,210,462,
%T A083482 506,276,60,130,234,126,406,870,930,248,264,1122,1190,210,222,1406,
%U A083482 1482,780,820,1722,1806,946,330,690,2162,564,84,70,510,1326,1378,954,990
%N A083482 Square root of smallest square of the type n(n+1)*k.
%C A083482 Squares pertaining to A083481.
%C A083482 a(n) == (p*q*r... ) where p,q,r are prime factors of n(n+1).
%H A083482 Ivan Neretin, <a href="/A083482/b083482.txt">Table of n, a(n) for n = 1..10000</a>
%F A083482 a(n) = sqrt(A002378(n)*A083481(n)) = sqrt(A002378(n)*A007913(A002378(n))). a(n) = A019554(A002378(n)). - _David Wasserman_, Nov 16 2004
%t A083482 Table[Times @@ ((a = Transpose[FactorInteger[n (n + 1)]])[[1]]^Quotient[a[[2]] + 1, 2]), {n, 54}] (* _Ivan Neretin_, May 20 2015 *)
%o A083482 (PARI) a(n)=sqrt(n*(n+1)*core(n*(n+1)))
%o A083482 (Python)
%o A083482 from math import prod
%o A083482 from sympy import factorint
%o A083482 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 A083482 Cf. A083481.
%K A083482 nonn
%O A083482 1,1
%A A083482 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003
%E A083482 More terms from _Benoit Cloitre_, May 04 2003
%E A083482 More terms from _David Wasserman_, Nov 16 2004