[seqfan] even/odd partitions of n into distinct primes

Richard Mathar mathar at strw.leidenuniv.nl
Sun Jan 9 18:05:44 CET 2011


It seems the two sequences
a(n) = (A000586(n) +/- A046675(n))/2
representing the number of even and odd partitions of n into
distinct primes are not in the OEIS (?)

The seem to start
1,0,0,0,0,1,0,1,1,1,1,0,1,1,1,1,2,1,2,1,2,2,2,2,3,3,3,2,3,3,3,4,4,5,5,4,6,5,5,
6,7,7,8,7,9,8,9,8,11,11,12,10,13,12,14,14,15,16,17,16,20,19,20,20,24,22,26,23,
27,27,30,28,34,33,36,34,40,37,43,41,46,46,50,

0,0,1,1,0,1,0,1,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,3,2,2,3,3,3,4,3,5,3,4,4,5,5,6,6,
7,5,7,7,8,8,8,9,11,9,10,11,12,12,14,13,16,14,16,15,19,17,20,20,22,20,23,24,27,
26,28,27,33,30,34,34,37,36,41,40,46,43,47,46,

Someone with a passionate addiction to number theory might take a look and
submit them if they are felt missing...
I didn't look at the equivalent splitting of A000607.



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