A271368 Number of ways to write n as the sum of distinct super-primes (A006450).

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, 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, 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

Offset: 1

Author

Felix Fröhlich, Apr 05 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• R. E. Dressler and S. T. Parker, Primes with a Prime Subscript, Journal of the ACM, Vol. 22, No. 3 (1975), 380-381.
• Wikipedia, Super-prime

Crossrefs

Cf. A000586, A006450.

Programs

PARI

isokp(pt) = {for (k=1, #pt, if (! isprime(pt[k]) || !isprime(primepi(pt[k])), return (0));); #pt == #Set(pt);}
a(n) = {if (n < 3, return (0)); nb = 0; forpart(pt = n, if (isokp(pt), nb++), [3, n]); nb;} \\ Michel Marcus, Apr 06 2016

Formula

G.f.: prod(k>=1, 1 + x^A006450(k) ). [Joerg Arndt, Apr 06 2016]

Extensions

More terms from Michel Marcus, Apr 06 2016