A067432 - OEIS

%I #14 Feb 05 2021 05:04:07

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

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

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

%N Number of ways to represent the n-th prime in form p*q+p+q, where p and q are primes (see A066938).

%C a(A049084(A066938(n))) > 0; a(A049084(A198273(n))) = 0; a(A049084(A198277(n))) = n and a(A049084(m)) <> n for m < A198277(n). [_Reinhard Zumkeller_, Oct 23 2011]

%C a(n) < A072670(n).

%H Reinhard Zumkeller, <a href="/A067432/b067432.txt">Table of n, a(n) for n = 1..10000</a>

%e a(15) = 2 as A000040(15) = 47 = 3*11+3+11 = 5*7+5+7.

%o (Haskell)

%o a067432 n = length [p | let prime_n = a000040 n,

%o    p <- takeWhile (< a000196 prime_n) a000040_list,

%o    let (q,m) = divMod (prime_n - p) (p + 1),

%o    m == 0, a010051 q == 1]

%o a067432_list = map a067432 [1..]

%o -- _Reinhard Zumkeller_, Oct 23 2011

%Y Cf. A000196, A010051.

%K nonn

%O 1,9

%A _Reinhard Zumkeller_, Feb 15 2002