A361671 Squarefree part of the n-th tetrahedral number.

1, 1, 10, 5, 35, 14, 21, 30, 165, 55, 286, 91, 455, 35, 170, 51, 969, 285, 1330, 385, 1771, 506, 23, 26, 13, 91, 406, 1015, 4495, 310, 341, 374, 6545, 1785, 7770, 2109, 9139, 2470, 2665, 2870, 12341, 3311, 14190, 3795, 16215, 1081, 94, 1, 17, 221, 23426, 689, 2915, 770, 7315, 7714, 32509, 8555

Offset: 1

Author

R. J. Mathar, Mar 20 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A007913, A000292, A361670 (of triangular), A083481 (of oblong).

Cf. A003556 (squarefree part is 1).

Programs

PARI

a(n) = core(n*(n+1)*(n+2)/6); \\ Michel Marcus, Mar 22 2023

Python

from sympy.ntheory.factor_ import core
def A361671(n): return core(n*(n*(n + 3) + 2)//6) # Chai Wah Wu, Mar 20 2023

Formula

a(n) = A007913(A000292(n)).