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a(n) = denominator((prime(n)-1)/prime(n)#), where prime(n)# = A002110(n) is the n-th primorial.
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%I #14 Jul 30 2022 08:18:39

%S 2,3,15,35,231,5005,255255,1616615,10140585,462120945,6685349671,

%T 1236789689135,30425026352721,311494317420715,13367169186706335,

%U 1253429172199617105,33151040519900217915,3909612711980232366109,119065478046670712967865,7970583287524270870963077

%N a(n) = denominator((prime(n)-1)/prime(n)#), where prime(n)# = A002110(n) is the n-th primorial.

%C See A356093 for details.

%H Amiram Eldar, <a href="/A356094/b356094.txt">Table of n, a(n) for n = 1..351</a>

%t primorial[n_] := Product[Prime[i], {i, 1, n}]; Denominator[Table[(Prime[i] - 1)/primorial[i], {i, 1, 20}]]

%o (PARI) a(n) = denominator((prime(n)-1)/factorback(primes(n))); \\ _Michel Marcus_, Jul 26 2022

%o (Python)

%o from math import gcd

%o from sympy import primorial, prime

%o def A356094(n): return (p:=primorial(n))//gcd(p,prime(n)-1) # _Chai Wah Wu_, Jul 26 2022

%Y Cf. A002110, A356093 (numerators).

%Y Similar sequences: A038111, A338560, A340819, A341432, A342451, A342480.

%K nonn,frac

%O 1,1

%A _Amiram Eldar_, Jul 26 2022