A325838 a(n) is the product of divisors of the n-th triangular number.

1, 3, 36, 100, 225, 441, 21952, 10077696, 91125, 3025, 18974736, 37015056, 8281, 121550625, 42998169600000000, 342102016, 3581577, 5000211, 1303210000, 3782285936100000000, 2847396321, 64009, 442032795979776, 19683000000000000000000, 34328125, 15178486401

Offset: 1

Author

Jaroslav Krizek, Sep 07 2019

Keywords

• nonn

Examples

			The 5th triangular number is 15, whose divisors are {1, 3, 5, 15}; their product is 225.
		

Crossrefs

Cf. A000005, A000203, A000217, A007955.

See A063440 and A074285 for number and sum of such divisors.

Programs

Magma

[&*[d: d in Divisors(n * (n+1) div 2)] : n in [1..1000]];

Mathematica

pd[n_] := n^(DivisorSigma[0, n]/2); t[n_] := n (n + 1)/2; pd /@ t /@ Range[26] (* Amiram Eldar, Sep 07 2019 *)

PARI

a(n) = vecprod(divisors(n*(n+1)/2)); \\ Michel Marcus, Oct 14 2019

Python

from math import isqrt
from sympy import divisor_count
def A325838(n): return (lambda m:(isqrt(m) if (c:=divisor_count(m)) & 1 else 1)*m**(c//2))(n*(n+1)//2) # Chai Wah Wu, Jun 25 2022

Formula

a(n) = A007955(A000217(n)).