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

%I A325838 #28 Jun 19 2025 14:39:00
%S A325838 1,3,36,100,225,441,21952,10077696,91125,3025,18974736,37015056,8281,
%T A325838 121550625,42998169600000000,342102016,3581577,5000211,1303210000,
%U A325838 3782285936100000000,2847396321,64009,442032795979776,19683000000000000000000,34328125,15178486401
%N A325838 a(n) is the product of divisors of the n-th triangular number.
%F A325838 a(n) = A007955(A000217(n)).
%e A325838 The 5th triangular number is 15, whose divisors are {1, 3, 5, 15}; their product is 225.
%t A325838 pd[n_] := n^(DivisorSigma[0, n]/2); t[n_] := n (n + 1)/2; pd /@ t /@ Range[26] (* _Amiram Eldar_, Sep 07 2019 *)
%o A325838 (Magma) [&*[d: d in Divisors(n * (n+1) div 2)] : n in [1..1000]];
%o A325838 (PARI) a(n) = vecprod(divisors(n*(n+1)/2)); \\ _Michel Marcus_, Oct 14 2019
%o A325838 (Python)
%o A325838 from math import isqrt
%o A325838 from sympy import divisor_count
%o A325838 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
%Y A325838 Cf. A000005, A000203, A000217, A007955.
%Y A325838 See A063440 and A074285 for number and sum of such divisors.
%K A325838 nonn
%O A325838 1,2
%A A325838 _Jaroslav Krizek_, Sep 07 2019