A235051 a(n) = |{0 < k < n-2: C(sigma(k) + phi(n-k)/2) - 1 is prime}|, where C(j) is the j-th Catalan number (A000108), sigma(k) is the sum of all positive divisors of k, and phi(.) is Euler's totient function.
0, 0, 0, 0, 1, 2, 3, 4, 3, 5, 3, 4, 4, 4, 5, 3, 4, 4, 5, 3, 2, 1, 4, 2, 2, 2, 4, 2, 2, 2, 2, 4, 5, 1, 1, 1, 3, 1, 2, 2, 5, 1, 1, 3, 1, 2, 1, 2, 1, 4, 3, 3, 3, 1, 0, 0, 2, 2, 2, 1, 7, 1, 0, 4, 1, 3, 1, 1, 2, 2, 1, 7, 4, 4, 1, 3, 3, 2, 3, 4, 3, 1, 7, 1, 5, 2, 5, 1, 3, 3, 4, 5, 1, 4, 2, 3, 4, 6, 5, 3
Offset: 1
Keywords
Examples
a(22) = 1 since sigma(8) + phi(14)/2 = 15 + 6/2 = 18 with C(18) - 1 = 477638699 prime.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..1800
Programs
-
Mathematica
sigma[n_]:=DivisorSigma[1,n] f[n_,k_]:=CatalanNumber[sigma[k]+EulerPhi[n-k]/2]-1 a[n_]:=Sum[If[PrimeQ[f[n,k]],1,0],{k,1,n-3}] Table[a[n],{n,1,100}] -
PARI
C(n)=binomial(2*n, n)/(n+1) a(n)=sum(k=1,n-3,ispseudoprime(C(sigma(k)+eulerphi(n-k)/2)-1)) \\ Charles R Greathouse IV, Jan 03 2014
Comments