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A325838
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a(n) is the product of divisors of the n-th triangular number.
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1
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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The 5th triangular number is 15, whose divisors are {1, 3, 5, 15}; their product is 225.
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MATHEMATICA
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pd[n_] := n^(DivisorSigma[0, n]/2); t[n_] := n (n + 1)/2; pd /@ t /@ Range[26] (* Amiram Eldar, Sep 07 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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