A361670 - OEIS

%I #14 Mar 23 2023 03:45:18

%S 1,3,6,10,15,21,7,1,5,55,66,78,91,105,30,34,17,19,190,210,231,253,69,

%T 3,13,39,42,406,435,465,31,33,561,595,70,74,703,741,195,205,861,903,

%U 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 Squarefree part of the n-th triangular number.

%C 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 a(n) = 1 for n>0 in A001108. - _Michel Marcus_, Mar 22 2023

%F a(n) = A007913(A000217(n)).

%p a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(n*(n+1)/2)[2]):

%p seq(a(n), n=1..70);  # _Alois P. Heinz_, Mar 20 2023

%o (Python)

%o from sympy.ntheory.factor_ import core

%o def A361670(n): return core(n*(n+1)>>1) # _Chai Wah Wu_, Mar 20 2023

%o (PARI) a(n) = core(n*(n+1)/2); \\ _Michel Marcus_, Mar 22 2023

%Y Cf. A000217, A007913, A083481 (of oblong), A361671 (of tetrahedral).

%Y Cf. A001108, A039963.

%K nonn,easy

%O 1,2

%A _R. J. Mathar_, Mar 20 2023