A347419 Number of partitions of n into two or more distinct primes.
0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 2, 1, 2, 2, 3, 1, 4, 2, 4, 4, 4, 4, 5, 5, 6, 5, 6, 6, 6, 8, 7, 9, 9, 9, 11, 10, 11, 13, 12, 13, 15, 14, 17, 16, 18, 18, 20, 21, 23, 22, 25, 25, 27, 30, 29, 32, 32, 34, 37, 38, 40, 42, 44, 45, 50, 49, 53, 55, 57, 60, 64, 66, 70, 71, 76, 78, 83, 86, 89, 93, 96
Offset: 1
Keywords
Examples
a(5) = 1: 2+3. a(18) = 4: 11+7, 11+5+2, 13+5, 13+3+2.
Programs
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Maple
h:= proc(n) h(n):=`if`(n<2, 0, `if`(isprime(n), n, h(n-1))) end: b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<2, 0, b(n, h(i-1))+b(n-i, h(min(n-i, i-1))))) end: a:= n-> b(n, h(n-1)): seq(a(n), n=1..100); # Alois P. Heinz, Sep 03 2021 -
Mathematica
m = 24; Rest @ CoefficientList[Series[Product[(1 + x^Prime[k]), {k, 1, m}], {x, 0, Prime[m]}], x] - Table[Boole @ PrimeQ[n], {n, 1, Prime[m]}] (* Amiram Eldar, Sep 03 2021 *) -
Python
from sympy import isprime, primerange from functools import cache @cache def A000586(n, k=None): # after Charles R Greathouse IV if k == None: k = n if n < 1: return int(n == 0) return sum(A000586(n-p, p-1) for p in primerange(1, k+1)) def a(n): return A000586(n) - isprime(n) print([a(n) for n in range(1, 83)]) # Michael S. Branicky, Sep 03 2021
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