A171080 a(n) = Product_{3 <= p <= 2*n+1, p prime} p^floor(2*n / (p - 1)).

1, 3, 45, 945, 14175, 467775, 638512875, 1915538625, 488462349375, 194896477400625, 32157918771103125, 2218896395206115625, 3028793579456347828125, 9086380738369043484375, 3952575621190533915703125, 28304394023345413370350078125, 7217620475953080409439269921875

Offset: 0

Author

N. J. A. Sloane, Sep 06 2010

Keywords

• nonn

References

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

Links

• Victor M. Buchstaber, Alexander P. Veselov, Todd polynomials and Hirzebruch numbers, arXiv:2310.07383 [math.AT], Oct. 2023.

Crossrefs

Cf. A091137, A238963, A160014.

Programs

Maple

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;

Mathematica

a[n_] := Product[If[PrimeQ[q], q^Floor[2 n/(q - 1)], 1], {q, 3, 2 n + 1}]
Table[a[n], {n, 0, 20}] (* Wolfgang Hintze, Oct 03 2014 *)

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

Formula

From Peter Luschny, Dec 12 2023: (Start)

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)