OFFSET
1,3
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1201 terms from Seth Troisi)
FORMULA
a(n) = A000586(prime(n)). - R. J. Mathar, Apr 30 2007
EXAMPLE
With the 10th prime 29, for instance, we have a(10)=7 distinct-prime partitions, viz. 29 = 2 + 3 + 7 + 17 = 2 + 3 + 5 + 19 = 2 + 3 + 11 + 13 = 3 + 7 + 19 = 5 + 7 + 17 = 5 + 11 + 13.
MATHEMATICA
nn = PrimePi[300]; t = CoefficientList[Series[Product[(1 + x^Prime[k]), {k, nn}], {x, 0, Prime[nn]}], x]; t[[1 + Prime[Range[nn]]]] (* T. D. Noe, Nov 13 2013 *)
PROG
(Haskell)
a070215 = a000586 . a000040 -- Reinhard Zumkeller, Aug 05 2012
(Python)
from sympy import sieve
from functools import cache
@cache
def b(n, k=None): # A000586
if k == None: k = n
if n < 1: return int(n == 0)
return sum(b(n-p, p-1) for p in sieve.primerange(1, k+1))
def a(n): return b(sieve[n])
print([a(n) for n in range(1, 54)]) # Michael S. Branicky, Nov 30 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, May 07 2002
EXTENSIONS
More terms from Naohiro Nomoto and Don Reble, May 11 2002
Offset in b-file corrected by N. J. A. Sloane, Aug 31 2009
STATUS
approved
