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%I #36 Mar 20 2023 10:10:30
%S 2,6,3,5,30,42,14,2,10,110,33,39,182,210,15,17,34,38,95,105,462,506,
%T 138,6,26,78,21,203,870,930,62,66,1122,1190,35,37,1406,1482,390,410,
%U 1722,1806,473,55,230,2162,141,3,2,102,663,689,318,330,770,798,3306,3422,885
%N Squarefree part of the n-th oblong number.
%C Smallest k such that n*(n+1)*k is a perfect square.
%C k = p*q*r... is a squarefree number where p,q,r are those prime factors of n(n+1) which have odd index.
%H Harvey P. Dale, <a href="/A083481/b083481.txt">Table of n, a(n) for n = 1..500</a>
%H John M. Campbell, <a href="http://arxiv.org/abs/1105.3399">An Integral Representation of Kekulé Numbers, and Double Integrals Related to Smarandache Sequences</a>, arXiv preprint arXiv:1105.3399 [math.GM], 2011.
%F a(n) = A007913(n*(n+1)). - _R. J. Mathar_, Nov 02 2011
%p A083481 := proc(n)
%p A007913(n)*A007913(n+1) ;
%p end proc:
%p seq( A083481(n),n=1..40) ; # _R. J. Mathar_, Mar 15 2023
%t 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 *)
%o (PARI) a(n)=core(n*(n+1))
%o (Python)
%o from sympy.ntheory.factor_ import core
%o def A083481(n): return core(n*(n+1)) # _Chai Wah Wu_, Mar 20 2023
%Y Cf. A002378, A007913, A083482.
%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
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