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, 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

Author

Juri-Stepan Gerasimov, Jul 23 2012

Keywords

• nonn
• tabf
• less

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,..

Examples

			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