A361670 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

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

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.