A214154 -id:A214154 - cp's OEIS frontend

A214026 Numbers n such that 2n is the average of two distinct k-almost primes (generalization of semiprimes) in more ways than for any smaller even number.

1, 4, 5, 8, 10, 12, 15, 18, 24, 30, 36, 45, 48, 60, 72, 84, 90, 120, 144, 168, 180, 210, 240, 288, 300, 330, 336, 360, 420, 480, 504, 540, 600, 630, 720

Offset: 1

Juri-Stepan Gerasimov, Jul 13 2012

Positions of records in A214154.

Cf. A002375, A045917, A053033, A214154.

A214364 Irregular triangle read by rows n lists the values k of all decompositions of 2n into unordered sums of two k-almost primes.

Original entry on oeis.org

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

Juri-Stepan Gerasimov, Jul 23 2012

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,..

			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.

Cf. A078840. - N. J. A. Sloane, Jul 29 2012

cp's OEIS Frontend

A214026 Numbers n such that 2n is the average of two distinct k-almost primes (generalization of semiprimes) in more ways than for any smaller even number.

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