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A214364
Irregular triangle read by rows n lists the values k of all decompositions of 2n into unordered sums of two k-almost primes.
0
0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 3, 2, 1, 1, 2, 1, 2, 1, 3, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 3, 1, 2, 2, 1, 2, 1, 3, 1, 2, 1, 2, 2, 3, 1, 4, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 3, 2, 1, 3, 3, 1, 1, 2, 1, 3, 2, 2, 4, 1, 3, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 2, 1, 2
OFFSET
1,5
COMMENTS
Row n has 1+A214154(n) entries, if n <> 1, where the '1' means the splitting 2*n=n+n into non-distinct k-almost primes is also registered here, but not in A214154. Therefore the last entry in row n is A001222(n) for n > 3.
Row sums are 0, 1, 1, 3, 4, 3, 4, 7, 6, 9, 3, 10, 8, 9, 12, 13, 6, 16, 10, 19, 12, 11, 9, 25, 16, 16, 15, 19, 14, 31, 14, 30, 14, 15, 24,..
EXAMPLE
If written as a triangle:
0,
1,
1,
1, 2,
1, 2, 1,
1, 2,
1, 2, 1,
1, 1, 2, 3,
2, 1, 1, 2,
1, 2, 1, 3, 2,
1, 1, 1,
1, 1, 2, 2, 1, 3,
1, 2, 1, 3, 1,
1, 2, 3, 1, 2,
2, 1, 2, 1, 3, 1, 2,
1, 2, 2, 3, 1, 4,
1, 1, 2, 1, 1,
1, 1, 3, 2, 1, 2, 2, 1, 3.
CROSSREFS
Cf. A078840. - N. J. A. Sloane, Jul 29 2012
Sequence in context: A300983 A279205 A105690 * A175922 A214856 A006337
KEYWORD
nonn,tabf,less
AUTHOR
STATUS
approved