A110936 a(n) = denominator(Bernoulli(prime(n) - 1))/prime(n).

1, 2, 6, 6, 6, 210, 30, 42, 6, 30, 462, 51870, 330, 42, 6, 30, 6, 930930, 966, 66, 1919190, 42, 6, 690, 46410, 330, 42, 6, 1919190, 14790, 34314, 66, 30, 1974, 30, 14322, 11430510, 798, 6, 30, 6, 39921071190, 66, 4501770, 870, 1229718, 43725066, 42, 6

Offset: 1

Author

Vladeta Jovovic, Jan 21 2006

Keywords

• easy
• nonn
• frac

Examples

			From _Peter Luschny_, Mar 30 2019: (Start)
n = 12 -> prime(12) - 1 = 37 - 1 = 36,
D = divisors(36) \ {36} = {1, 2, 3, 4, 6, 9, 12, 18},
P = {p: (p-1) in D, p prime} = {2, 3, 5, 7, 13, 19},
Product(P) = 51870 = a(n).
.
n = 18 -> prime(18) - 1 = 61 - 1 = 60,
D = divisors(60) \ {60} = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30},
P = {p: (p-1) in D, p prime} = = {2, 3, 5, 7, 11, 13, 31},
Product(P) = 930930 = a(n).
(End)
		

Crossrefs

Cf. A000040, A002445.

Programs

Maple

a := proc(n) if not isprime(n+1) then return NULL fi;
numtheory[divisors](n) minus {n};
map(i->i+1, %); mul(i, i=select(isprime, %)) end:
seq(a(n), n=1..226); # Peter Luschny, Mar 30 2019

Mathematica

a[n_] := (p = Prime[n]; Denominator[ BernoulliB[p - 1]]/p); Table[a[n], {n, 1, 49}] (* Jean-François Alcover, Dec 13 2012 *)

Formula

6 divides a(n) for n >= 3. a(n) is squarefree. - Peter Luschny, Mar 30 2019