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A361670
Squarefree part of the n-th triangular number.
2
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
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).
Sequence in context: A138777 A096895 A034175 * A368825 A306698 A139131
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 20 2023
STATUS
approved