|
%I #29 Apr 18 2023 08:30:00
%S 3,20,42,7920,156,57120,342,212520,342014400,930,1673844480,2430480,
%T 1806,4280760,16529385600,32441381280,3660,71852901120,23319240,5256,
%U 200133133200,44102880,418397031360,5827054819622400,97990200,10506,123854640,11772,154529760
%N a(n) = product of numbers from prime(n)+1 up to prime(n+1), where prime(n) is the n-th prime.
%C Originally the offset was -1 and two terms more in front were pre defined in a inscrutable manner (a(-1)=1, a(0) = 2; .....). - _Karl-Heinz Hofmann_, Apr 18 2023
%H Karl-Heinz Hofmann, <a href="/A072472/b072472.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000040(n+1)*A061214(n). - _Karl-Heinz Hofmann_, Apr 18 2023
%e a(1) = 3
%e a(2) = 4 * 5 = 20
%e a(3) = 6 * 7 = 42
%e a(4) = 8 * 9 * 10 * 11 = 7920
%t a[n_] := Product[k, {k, Prime[n] + 1, Prime[n + 1]}]; Table[a[n], {n, 1, 30}]
%o (Python)
%o from sympy import prod, sieve as prime
%o def A072472(n):
%o return prod(range(prime[n]+1, prime[n+1]+1)) # _Karl-Heinz Hofmann_, Apr 17 2023
%o (PARI) a(n) = prod(k=prime(n)+1, prime(n+1), k); \\ _Michel Marcus_, Apr 17 2023
%Y Cf. A000040, A061214, A361760, A361761.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Jun 20 2002
%E Edited by _Robert G. Wilson v_, Jun 21 2002
%E Offset, data and name corrected by _Karl-Heinz Hofmann_, Apr 18 2023
|
