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a(n) = Product_{3 <= p <= 2*n+1, p prime} p^floor(2*n / (p - 1)).
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%I #30 Dec 14 2023 16:28:55

%S 1,3,45,945,14175,467775,638512875,1915538625,488462349375,

%T 194896477400625,32157918771103125,2218896395206115625,

%U 3028793579456347828125,9086380738369043484375,3952575621190533915703125,28304394023345413370350078125,7217620475953080409439269921875

%N a(n) = Product_{3 <= p <= 2*n+1, p prime} p^floor(2*n / (p - 1)).

%D F. Hirzebruch, Topological Methods in Algebraic Geometry, Springer, 3rd. ed., 1966; Lemma 1.5.2, p. 13.

%H Victor M. Buchstaber, Alexander P. Veselov, <a href="https://doi.org/10.48550/arXiv.2310.07383">Todd polynomials and Hirzebruch numbers</a>, arXiv:2310.07383 [math.AT], Oct. 2023.

%F From _Peter Luschny_, Dec 12 2023: (Start)

%F a(n) = (Clausen(2*n)*a(n-1))/2 for n > 0, where Clausen(n) = A160014(1, n).

%F a(n) = A091137(2*n) / 2^(2*n). (End)

%p 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;

%t a[n_] := Product[If[PrimeQ[q], q^Floor[2 n/(q - 1)], 1], {q, 3, 2 n + 1}]

%t Table[a[n], {n, 0, 20}] (* _Wolfgang Hintze_, Oct 03 2014 *)

%o (SageMath)

%o from functools import cache

%o @cache

%o def a_rec(n):

%o if n == 0: return 1

%o p = mul(s for s in map(lambda i: i+1, divisors(2*n)) if is_prime(s))

%o return (p * a_rec(n - 1)) // 2

%o print([a_rec(n) for n in range(17)]) # _Peter Luschny_, Dec 12 2023

%Y Cf. A091137, A238963, A160014.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Sep 06 2010