A345300 a(n) is the number of distinct primes of the form n + A - B where A and B are sums of subsets of the prime factors of n.

0, 1, 1, 1, 1, 4, 1, 0, 0, 5, 1, 4, 1, 4, 4, 0, 1, 4, 1, 3, 3, 3, 1, 3, 0, 4, 0, 3, 1, 4, 1, 0, 3, 3, 3, 3, 1, 3, 2, 3, 1, 4, 1, 2, 4, 3, 1, 3, 0, 3, 3, 3, 1, 2, 2, 2, 3, 3, 1, 4, 1, 2, 4, 0, 3, 5, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 2, 5, 1, 2, 0, 2, 1, 3, 3, 4, 2, 3, 1, 3, 2, 3, 2, 2, 2, 2, 1, 3, 2

Offset

1,6

Comments

If n is prime, a(n) = 1.

If n is a prime power other than 4, a(n) = 0.

Links

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

Example

a(6) = 4 because there are four such primes: 3 = 6-3, 5 = 6+2-3, 7 = 6+3-2, and 11=6+2+3.

Maple

f:= proc(n) local S, p;
  S:= {n};
  for p in numtheory:-factorset(n) do
    S:= S union map(`+`, S, p) union map(`-`, S, p)
  od:
  nops(select(isprime, S))
end proc:
map(f, [$1..1000]);

Crossrefs

Cf. A345316.

Sequence in context: A221971 A297785 A334702 * A085992 A117411 A161739

Adjacent sequences: A345297 A345298 A345299 * A345301 A345302 A345303

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jun 13 2021

Status

approved