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A157188 Number of ways to write prime(n) as p*q-(p+q) with primes p<=q. 3


%S 0,2,1,1,2,0,1,1,2,1,1,0,1,1,1,0,3,0,0,4,0,1,1,0,0,1,1,2,0,0,0,2,1,1,

%T 1,0,0,1,2,0,3,0,3,0,1,1,1,1,1,0,0,3,0,2,0,2,1,1,0,1,0,0,0,4,0,0,1,0,

%U 2,0,0,4,0,0,1,2,0,0,0,0,4,0,4,0,0,1,0,0,1,1,1,3,0,1,1,3,0,1,1,0,0,0,1,1,0

%N Number of ways to write prime(n) as p*q-(p+q) with primes p<=q.

%C Records in this sequence are given in A157189, the corresponding primes in A157190.

%H C. Rivera (Ed.), <a href="http://www.primepuzzles.net/puzzles/puzz_482.htm">Puzzle 482: Two Bergot questions</a>, March 2009.

%e a(1)=0 since prime(1) = 2 cannot be written as pq-(p+q) for primes p,q.

%e a(2)=2 since prime(2) = 3 = 2*5-(2+5) = 3*3-(3+3) are the two possibilities.

%o (PARI) A157188(n)={ local(c=0,L=sqrtint(n=prime(n)+1)); fordiv( n,d, d>L&break; isprime(d+1) | next; isprime(n/d+1) & c++);c}

%Y Cf. A157187-A157190

%K nonn

%O 1,2

%A _M. F. Hasler_, Mar 11 2009

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Last modified March 25 03:37 EDT 2023. Contains 361511 sequences. (Running on oeis4.)