login
a(n) = A058254(n+1)/A058254(n).
1

%I #18 Mar 22 2020 05:48:20

%S 2,2,3,5,1,4,3,11,7,1,1,1,1,23,13,29,1,1,1,1,1,41,1,2,5,17,53,3,1,1,1,

%T 1,1,37,1,1,3,83,43,89,1,19,2,7,1,1,1,113,1,1,1,1,5,4,131,67,1,1,1,47,

%U 73,1,31,1,79,1,1,173,1,1,179,61,1,1,191,97,1,1,1,1,1,1,1,1,1,1,1,1,1

%N a(n) = A058254(n+1)/A058254(n).

%C a(n) = 1 if in prime(n+1)-1 no new prime divisor or new power of a prime appear, like LCM[{1, 2, 4, 6, 10, 12, 16, 22}]= LCM[{1, 2, 4, 6, 10, 12, 16, 22, 28}].

%C a(n) > 1 if in prime(n+1)-1 new prime divisor(s) or new power(s) of a prime arise, like in A058254(15) compared with A058254(14), where the new prime divisor is 23 only, so a(14)=23. Such sites of increase do not correspond to the natural order of primes and prime-powers like in A054451.

%H Amiram Eldar, <a href="/A058256/b058256.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = lcm{i=1..n+1} (prime(i)-1) / lcm{i=1..n} (prime(i)-1).

%o (PARI) f(n) = lcm(apply(p->p-1, primes(n))); \\ A058254

%o a(n) = f(n+1)/f(n); \\ _Michel Marcus_, Mar 22 2020

%Y Cf. A058254, A002110, A005867, A003418, A054451, A000142, A000010, A003418, A000961.

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 06 2000

%E Offset corrected by _Amiram Eldar_, Sep 24 2019