A058256 a(n) = A058254(n+1)/A058254(n).

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, 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, 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

Offset: 1

Author

Labos Elemer, Dec 06 2000

Keywords

• nonn

Comments

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}].

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

PARI

f(n) = lcm(apply(p->p-1, primes(n))); \\ A058254
a(n) = f(n+1)/f(n); \\ Michel Marcus, Mar 22 2020

Formula

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

Extensions

Offset corrected by Amiram Eldar, Sep 24 2019