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

1,31

Comments

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

Links

Table of n, a(n) for n=1..100.

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A000586, A006450.

Sequence in context: A216266 A177416 A087606 * A116799 A057556 A112761

Adjacent sequences: A271365 A271366 A271367 * A271369 A271370 A271371

Keyword

nonn

Author

Felix Fröhlich, Apr 05 2016

Extensions

More terms from Michel Marcus, Apr 06 2016

Status

approved