A184833 a(n) = largest k such that A005117(n+1) = A005117(n) + (A005117(n) mod k), or 0 if no such k exists.

0, 0, 0, 4, 5, 4, 9, 9, 12, 13, 13, 15, 17, 20, 21, 20, 23, 28, 29, 29, 32, 33, 33, 36, 37, 37, 40, 41, 40, 45, 43, 49, 51, 53, 56, 57, 57, 60, 59, 64, 65, 65, 68, 69, 69, 72, 71, 76, 77, 76, 81, 81, 84, 85, 85, 87, 89, 92, 93, 93, 93, 100, 101, 101, 104, 105

Offset: 1

Author

Rémi Eismann, Jan 23 2011

Keywords

• nonn
• easy

Comments

From the definition, a(n) = A005117(n) - A076259(n) if A005117(n) - A076259(n) > A076259(n), 0 otherwise where A005117 are the squarefree numbers and A076259 are the gaps between squarefree numbers.

Examples

			For n = 1 we have A005117(1) = 1, A005117(2) = 2; there is no k such that 2 - 1 = 1 = (1 mod k), hence a(1) = 0.
For n = 4 we have A005117(4) = 5, A005117(5) = 6; 4 is the largest k such that 6 - 5 = 1 = (5 mod k), hence a(4) = 2; a(3) = 5 - 1 = 4.
For n = 23 we have A005117(23) = 35, A005117(24) = 37; 33 is the largest k such that 37 - 35 = 2 = (35 mod k), hence a(23) = 33; a(24) = 35 - 2 = 33.
		

Links

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

Crossrefs

Cf. A005117, A076259, A184832, A184834, A117078, A117563, A001223, A118534.