A325838 - OEIS

%I #23 Jun 25 2022 21:54:52

%S 1,3,36,100,225,441,21952,10077696,91125,3025,18974736,37015056,8281,

%T 121550625,42998169600000000,342102016,3581577,5000211,1303210000,

%U 3782285936100000000,2847396321,64009,442032795979776,19683000000000000000000,34328125,15178486401

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

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

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

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

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

%o (PARI) a(n) = vecprod(divisors(n*(n+1)/2)); \\ _Michel Marcus_, Oct 14 2019

%o (Python)

%o from math import isqrt, divisor_count

%o 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 Cf. A000005, A000203, A000217, A007955.

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

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Sep 07 2019