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A344788
a(n) is the number of pairs of primes (q,r) with prime(n) > q > r such that q | r + prime(n) and r | q + prime(n).
2
0, 0, 0, 2, 1, 2, 0, 3, 3, 0, 3, 3, 0, 3, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 3, 1, 4, 1, 2, 2, 3, 4, 1, 3, 2, 3, 3, 5, 3, 2, 4, 3, 2, 3, 0, 3, 3, 3, 0, 4, 4, 2, 1, 4, 3, 6, 0, 4, 3, 0, 4, 3, 4, 3, 3, 3, 3, 4, 2, 3, 2, 5, 4, 5, 3, 5, 3, 4, 3, 2, 3, 3, 5, 3, 3, 4, 2, 4, 0, 4, 3, 6, 3, 5, 3, 5, 2, 1, 4
OFFSET
1,4
LINKS
EXAMPLE
a(8) = 3 because prime(8) = 19 and there are 3 pairs (3,2), (7,2), (11,3) with 3 | 2+19, 2 | 3+19, 7 | 2+19, 2 | 7+19, 11 | 3+19, 3 | 11+19.
MAPLE
f:= proc(n) local ia, a, b, c, t;
c:= ithprime(n);
t:= 0;
for ia from 1 to n-1 do
a:= ithprime(ia);
t:= t + nops(select(b -> b < c and b+c mod a = 0, numtheory:-factorset(a+c)))
od;
t/2
end proc:
map(f, [$1..100]);
CROSSREFS
Cf. A344776.
Sequence in context: A290537 A377087 A272569 * A372687 A068076 A138498
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, May 28 2021
STATUS
approved