|
|
A270992
|
|
Number of distinct prime divisors of prime(n)+1 and prime(n+1)+1.
|
|
2
|
|
|
0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,9
|
|
LINKS
|
|
|
EXAMPLE
|
For n=1, p=2 and q=3; 3 and 4 have no common prime divisor, so a(1)=0.
For n=2, p=3 and q=5; 4 and 6 have 1 common prime divisor, so a(2)=1.
For n=9, p=23 and q=29; 24 and 30 have 2 common prime divisors, so a(9)=2.
|
|
MATHEMATICA
|
Table[Length[Map[First, FactorInteger[GCD @@ {Prime@ n + 1, Prime[n + 1] + 1}]] /. 1 -> Nothing], {n, 101}] (* Michael De Vlieger, Mar 28 2016 *)
Length[Intersection[FactorInteger[#[[1]]+1][[All, 1]], FactorInteger[#[[2]] + 1][[All, 1]]]]&/@Partition[Prime[Range[120]], 2, 1] (* Harvey P. Dale, Jun 11 2017 *)
|
|
PROG
|
(PARI) lista(nn) = {p = 2; f = factor(p+1)[, 1]~; forprime(q=3, nn, g = factor(q+1)[, 1]~; print1(#setintersect(f, g), ", "); p = q; f = g; ); }
(PARI) a(n) = my(p = prime(n), q = nextprime(p+1)); #setintersect(factor(p+1)[, 1]~, factor(q+1)[, 1]~);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|