

A340996


a(n) is the number of different primes that can be expressed as n mod p where p < n is prime.


2



0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 1, 3, 2, 3, 2, 3, 1, 3, 2, 5, 2, 4, 2, 4, 3, 4, 3, 3, 4, 3, 1, 6, 3, 4, 2, 6, 3, 6, 3, 5, 4, 5, 4, 7, 4, 6, 4, 5, 3, 8, 3, 5, 3, 6, 4, 9, 3, 6, 5, 8, 4, 7, 2, 6, 4, 8, 4, 9, 5, 7, 5, 8, 3, 9, 5, 7, 7, 7, 4, 10, 5, 6, 5, 7, 6, 12, 5, 7, 7, 7, 4, 11, 5, 9
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,8


COMMENTS

a(n) is the number of primes p < n such that np has a prime factor > p.
a(n) <= A056172(n1), with equality for n = 1, 2, 3, 4, 5, 8, 24.


LINKS



EXAMPLE

a(8) = 2 because 2 = 8 mod 3 and 3 = 8 mod 5.


MAPLE

f:= proc(n) local k; nops(select(isprime, {seq(n mod k, k=select(isprime, [$2..n1]))})) end proc:
map(f, [$1..100]);


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



