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A083338
Number of partitions of odd numbers into three primes and of even numbers into two primes.
4
0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 2, 4, 2, 3, 2, 5, 3, 5, 3, 5, 3, 7, 2, 7, 3, 6, 2, 9, 4, 8, 4, 9, 2, 10, 3, 11, 4, 10, 3, 12, 4, 13, 5, 12, 4, 15, 3, 16, 5, 14, 3, 17, 4, 16, 6, 16, 3, 19, 5, 21, 6, 20, 2, 20, 5, 22, 6, 21, 5, 22, 5, 28, 7, 24, 4, 25, 5, 29, 8, 27, 5, 29, 4, 33, 9, 29, 4
OFFSET
1,9
COMMENTS
a(n) > 0 for all n iff Goldbach's conjectures hold.
FORMULA
a(n) = if n is even then A045917(n/2) else A054860((n-1)/2).
For even n: a(n) = A061358(n); for odd n: a(n) = A068307(n). - Antti Karttunen, Sep 14 2017
MATHEMATICA
f[n_] := Length@ IntegerPartitions[n, If[ OddQ@ n, {3}, {2}], Prime@ Range@ PrimePi@ n]; Array[f, 92] (* Robert G. Wilson v, Nov 28 2012 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Apr 24 2003
STATUS
approved