A184728 -id:A184728 - cp's OEIS frontend

A184729 a(n) = A184728(n)/A130533(n) unless A130533(n) = 0 in which case a(n) = 0.

0, 0, 4, 1, 1, 1, 10, 1, 12, 1, 16, 11, 8, 1, 4, 1, 1, 1, 1, 28, 9, 1, 1, 8, 1, 12, 1, 42, 17, 1, 1, 46, 31, 7, 1, 1, 28, 39, 39, 60, 11, 13, 25, 66, 1, 70, 47, 47, 72, 1, 38, 1, 1, 26, 1, 7, 88, 1, 1, 61, 20, 17, 100, 67, 67, 102, 29, 41, 106

Offset: 1

Rémi Eismann, Jan 20 2011

nonn

a(n) is the "level" of semiprimes.
The decomposition of semiprimes into weight * level + gap is A001358(n) = A130533(n) * a(n) + A065516(n) if a(n) > 0.
A184728(n) = A001358(n) - A065516(n) if A001358(n) - A065516(n) > A065516(n), 0 otherwise.

			For n = 1 we have A130533(1) = 0, hence a(1) = 0.
For n = 3 we have A184728(3)/A130533(3)= 8 / 2 = 4; hence a(3) = 4.
For n = 20 we have A184728(20)/A130533(20)= 56 / 2 = 28; hence a(20) = 28.

Rémi Eismann, Table of n, a(n) for n = 1..10000

Cf. A001358, A065516, A130533, A184728, A117078, A117563, A001223, A118534.

A130533 a(n) = smallest k such that A001358(n+1) = A001358(n) + (A001358(n) mod k), or 0 if no such k exists.

Original entry on oeis.org

0, 0, 2, 6, 13, 9, 2, 19, 2, 19, 2, 3, 4, 37, 8, 43, 47, 47, 53, 2, 6, 59, 61, 8, 71, 6, 79, 2, 5, 83, 89, 2, 3, 12, 101, 107, 4, 3, 3, 2, 11

Offset: 1

Rémi Eismann, Aug 16 2007 - Jan 20 2011

nonn

a(n) is the "weight" of semiprimes.

The decomposition of semiprimes into weight * level + gap is A001358(n) = a(n) * A184729(n) + A065516(n) if a(n) > 0.

			For n = 1 we have A001358(n) = 4, A001358(n+1) = 6; there is no k such that 6 - 4 = 2 = (4 mod k), hence a(1) = 0.
For n = 3 we have A001358(n) = 9, A001358(n+1) = 10; 2 is the smallest k such that 10 - 9 = 1 = (9 mod k), hence a(3) = 2.
For n = 19 we have A001358(n) = 55, A001358(n+1) = 57; 53 is the smallest k such that 57 - 55 = 2 = (55 mod k), hence a(19) = 53.

Remi Eismann, Table of n, a(n) for n=1..9999

Cf. A001358, A065516, A184729, A184728, A117078, A117563, A001223, A118534.

cp's OEIS Frontend

A184729 a(n) = A184728(n)/A130533(n) unless A130533(n) = 0 in which case a(n) = 0.

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