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A271368
Number of ways to write n as the sum of distinct super-primes (A006450).
1
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
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
Sequence in context: A216266 A177416 A087606 * A116799 A057556 A112761
KEYWORD
nonn
AUTHOR
Felix Fröhlich, Apr 05 2016
EXTENSIONS
More terms from Michel Marcus, Apr 06 2016
STATUS
approved