A184827 -id:A184827 - cp's OEIS frontend

A184828 a(n) = A184827(n)/A130889(n) unless A130889(n) = 0 in which case a(n) = 0.

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 13, 13, 1, 1, 1, 9, 3, 3, 11, 1, 1, 25, 25, 1, 3, 1, 13, 31, 1, 1, 3, 37, 1, 27, 1, 1, 7, 43, 5, 1, 1, 1, 1, 1, 17, 29, 1, 1, 1, 1, 3, 23, 5, 1, 45, 19, 19, 7, 31, 1, 5, 1, 1, 1, 43, 1, 31, 1, 5, 85, 85, 5, 1, 11, 43, 3

Offset: 1

Rémi Eismann, Jan 23 2011

nonn

a(n) is the "level" of lucky numbers.
The decomposition of lucky numbers into weight * level + gap is A000959(n) = A130889(n) * a(n) + A031883(n) if a(n) > 0.
A184827(n) = A000959(n) - A031883(n) if A000959(n) - A031883(n) > A031883(n), 0 otherwise.

			For n = 1 we have A130889(1) = 0, hence a(1) = 0.
For n = 3 we have A184752(3)/A130889(3)= 5 / 5 = 1; hence a(3) = 1.
For n = 24 we have A184752(24)/A130889(24)= 99 / 9 = 11; hence a(24) = 11.

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

Cf. A000959, A031883, A130889, A184827, A117078, A117563, A001223, A118534.

A130889 a(n) = smallest k such that A000959(n+1) = A000959(n) + (A000959(n) mod k), or 0 if no such k exists.

Original entry on oeis.org

0, 0, 5, 5, 11, 9, 17, 19, 29, 29, 31, 37, 47, 13, 59, 5, 5, 71, 71, 71, 9, 29, 31, 9, 107, 103, 5, 5, 131, 43, 131, 11, 5, 157, 167, 51, 5, 191, 7, 197, 199, 29, 5, 43, 227, 233, 233, 223, 257, 15, 9, 263, 281, 281, 281, 97, 13, 59, 317, 7, 17, 17, 47, 11, 353, 71, 349, 379, 389

Offset: 1

Rémi Eismann, Aug 21 2007 - Jan 23 2011

nonn

a(n) is the "weight" of lucky numbers.

The decomposition of lucky numbers into weight * level + gap is A000959(n) = a(n) * A184828(n) + A031883(n) if a(n) > 0.

			For n = 1 we have A000959(n) = 1, A000959(n+1) = 3; there is no k such that 3 - 1 = 2 = (1 mod k), hence a(1) = 0.
For n = 3 we have A000959(n) = 7, A000959(n+1) = 9; 5 is the smallest k such that 9 - 7 = 2 = (7 mod k), hence a(3) = 5.
For n = 24 we have A000959(n) = 105, A000959(n+1) = 111; 9 is the smallest k such that 111 - 105 = 6 = (105 mod k), hence a(24) = 9.

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

Cf. A000959, A031883, A184828, A184827, A117078, A117563, A001223, A118534.

cp's OEIS Frontend

A184828 a(n) = A184827(n)/A130889(n) unless A130889(n) = 0 in which case a(n) = 0.

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