cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A361670 Squarefree part of the n-th triangular number.

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%I A361670 #14 Mar 23 2023 03:45:18
%S A361670 1,3,6,10,15,21,7,1,5,55,66,78,91,105,30,34,17,19,190,210,231,253,69,
%T A361670 3,13,39,42,406,435,465,31,33,561,595,70,74,703,741,195,205,861,903,
%U A361670 946,110,115,1081,282,6,1,51,1326,1378,159,165,385,399,1653,1711,1770,1830,1891,217,14,130,2145,2211,2278
%N A361670 Squarefree part of the n-th triangular number.
%C A361670 a(n) / A083481(n) is either 2 or 1/2 depending on A136480(n) being even or odd, which is indicated by A039963(n).
%C A361670 a(n) = 1 for n>0 in A001108. - _Michel Marcus_, Mar 22 2023
%F A361670 a(n) = A007913(A000217(n)).
%p A361670 a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(n*(n+1)/2)[2]):
%p A361670 seq(a(n), n=1..70);  # _Alois P. Heinz_, Mar 20 2023
%o A361670 (Python)
%o A361670 from sympy.ntheory.factor_ import core
%o A361670 def A361670(n): return core(n*(n+1)>>1) # _Chai Wah Wu_, Mar 20 2023
%o A361670 (PARI) a(n) = core(n*(n+1)/2); \\ _Michel Marcus_, Mar 22 2023
%Y A361670 Cf. A000217, A007913, A083481 (of oblong), A361671 (of tetrahedral).
%Y A361670 Cf. A001108, A039963.
%K A361670 nonn,easy
%O A361670 1,2
%A A361670 _R. J. Mathar_, Mar 20 2023