A330768 a(n) is the number of divisors d of A014574(n) such that A014574(n)+d-1 and A014574(n)+d+1 are primes.

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

Offset

1,13

Links

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

Example

A014574(13) = 180.  Four of its divisors yield twin prime pairs when added to 179 and 181, namely 12, 18, 60 and 90, as 179+12=191, 181+12=193, 179+18=197, 181+18=199, 179+50=239, 181+60=241, 179+90=269 and 181+90=271 are prime.  Thus a(13)=4.

Maple

f:= proc(n)
    nops(select(t -> isprime(n+t) and isprime(n+2+t), numtheory:-divisors(n+1)))
end proc:
P:= select(isprime, {seq(i, i=3..50000, 2)}):
TP:= sort(convert(P intersect map(`-`, P, 2), list)):
map(f, TP);

Crossrefs

Cf. A014574.

Sequence in context: A277767 A107088 A137986 * A093486 A259618 A377036

Adjacent sequences: A330765 A330766 A330767 * A330769 A330770 A330771

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 29 2019

Status

approved