A361670 Squarefree part of the n-th triangular number.

1, 3, 6, 10, 15, 21, 7, 1, 5, 55, 66, 78, 91, 105, 30, 34, 17, 19, 190, 210, 231, 253, 69, 3, 13, 39, 42, 406, 435, 465, 31, 33, 561, 595, 70, 74, 703, 741, 195, 205, 861, 903, 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

Offset

1,2

Comments

a(n) / A083481(n) is either 2 or 1/2 depending on A136480(n) being even or odd, which is indicated by A039963(n).

a(n) = 1 for n>0 in A001108. - Michel Marcus, Mar 22 2023

Links

Table of n, a(n) for n=1..67.

Formula

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

Maple

a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(n*(n+1)/2)[2]):
seq(a(n), n=1..70);  # Alois P. Heinz, Mar 20 2023

Prog

(Python)
from sympy.ntheory.factor_ import core
def A361670(n): return core(n*(n+1)>>1) # Chai Wah Wu, Mar 20 2023
(PARI) a(n) = core(n*(n+1)/2); \\ Michel Marcus, Mar 22 2023

Crossrefs

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

Cf. A001108, A039963.

Sequence in context: A138777 A096895 A034175 * A368825 A306698 A139131

Adjacent sequences: A361667 A361668 A361669 * A361671 A361672 A361673

Keyword

nonn,easy

Author

R. J. Mathar, Mar 20 2023

Status

approved