A271368 - OEIS

%I #16 Apr 07 2016 16:20:01

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

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

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

%N Number of ways to write n as the sum of distinct super-primes (A006450).

%C a(n) > 0 for n > 96 (cf. Dressler, Parker, 1975).

%H R. E. Dressler and S. T. Parker, <a href="http://dx.doi.org/10.1145/321892.321900">Primes with a Prime Subscript</a>, Journal of the ACM, Vol. 22, No. 3 (1975), 380-381.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Super-prime">Super-prime</a>

%F G.f.: prod(k>=1, 1 + x^A006450(k) ). [_Joerg Arndt_, Apr 06 2016]

%e There are two ways to write 31 as the sum of distinct super-primes: 31 (a single summand, as 31 is itself a super-prime) and 17 + 11 + 3 (three summands), so a(31) = 2.

%o (PARI) isokp(pt) = {for (k=1, #pt, if (! isprime(pt[k]) || !isprime(primepi(pt[k])), return (0));); #pt == #Set(pt);}

%o a(n) = {if (n < 3, return (0)); nb = 0; forpart(pt = n, if (isokp(pt), nb++), [3, n]); nb;} \\ _Michel Marcus_, Apr 06 2016

%Y Cf. A000586, A006450.

%K nonn

%O 1,31

%A _Felix Fröhlich_, Apr 05 2016

%E More terms from _Michel Marcus_, Apr 06 2016