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A171080
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a(n) = Product_{3 <= p <= 2*n+1, p prime} p^floor(2*n / (p - 1)).
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5
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1, 3, 45, 945, 14175, 467775, 638512875, 1915538625, 488462349375, 194896477400625, 32157918771103125, 2218896395206115625, 3028793579456347828125, 9086380738369043484375, 3952575621190533915703125, 28304394023345413370350078125, 7217620475953080409439269921875
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OFFSET
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0,2
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REFERENCES
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F. Hirzebruch, Topological Methods in Algebraic Geometry, Springer, 3rd. ed., 1966; Lemma 1.5.2, p. 13.
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LINKS
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FORMULA
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a(n) = (Clausen(2*n)*a(n-1))/2 for n > 0, where Clausen(n) = A160014(1, n).
a(n) = A091137(2*n) / 2^(2*n). (End)
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MAPLE
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f:=proc(n) local q, t1; t1:=1; for q from 3 to 2*n+1 do if isprime(q) then t1:=t1*q^floor(2*n/(q-1)); fi; od; t1; end;
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MATHEMATICA
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a[n_] := Product[If[PrimeQ[q], q^Floor[2 n/(q - 1)], 1], {q, 3, 2 n + 1}]
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PROG
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(SageMath)
from functools import cache
@cache
def a_rec(n):
if n == 0: return 1
p = mul(s for s in map(lambda i: i+1, divisors(2*n)) if is_prime(s))
return (p * a_rec(n - 1)) // 2
print([a_rec(n) for n in range(17)]) # Peter Luschny, Dec 12 2023
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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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