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

1,2

Links

Table of n, a(n) for n=1..26.

Formula

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

Example

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

Mathematica

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

Prog

(Magma) [&*[d: d in Divisors(n * (n+1) div 2)] : n in [1..1000]]
(PARI) a(n) = vecprod(divisors(n*(n+1)/2)); \\ Michel Marcus, Oct 14 2019
(Python)
from math import isqrt, 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

Crossrefs

Cf. A000005, A000203, A000217, A007955.

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

Sequence in context: A158207 A227032 A153448 * A140958 A156189 A158077

Adjacent sequences: A325835 A325836 A325837 * A325839 A325840 A325841

Keyword

nonn

Author

Jaroslav Krizek, Sep 07 2019

Status

approved