A340743 a(n) is the number of primes that divide at least one of the numbers prime(n)-prime(k) for 1 <= k < n.

0, 0, 2, 2, 2, 4, 4, 4, 4, 5, 6, 6, 8, 7, 6, 7, 8, 8, 8, 9, 9, 10, 8, 11, 12, 10, 10, 10, 13, 13, 13, 13, 14, 14, 14, 15, 15, 16, 15, 13, 17, 17, 16, 18, 16, 17, 18, 20, 15, 21, 20, 21, 20, 20, 21, 19, 22, 22, 21, 24, 22, 21, 24, 23, 24, 22, 25, 28, 22, 26, 25, 24, 26, 28, 23, 25, 28, 28, 30, 30

Offset

1,3

Comments

Numbers not in the sequence appear to include 1, 3, 27, 51, 108, 218, 392, 486, 937.

a(n) >= the number of m with A340752(m) <= prime(n).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

For n=6 the a(6) = 4 primes are 2, 3, 5 and 11: 2 divides all but 13-2, 3 divides 13-8, 5 divides 13-3 and 11 divides 13-2.

Maple

f:= proc(n) local L, P, i, t;
  L:= [seq(ithprime(n)-ithprime(i), i=1..n-1)];
  P:= `union`(seq(numtheory:-factorset(t), t=L));
  nops(P)
end proc:
map(f, [$1..100]);

Crossrefs

Sequence in context: A106160 A305117 A283426 * A317841 A007614 A289256

Adjacent sequences: A340740 A340741 A340742 * A340744 A340745 A340746

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 18 2021

Status

approved