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%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
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