A303577 Break up the list of values of the divisor function d(k) into nondecreasing runs; sequence gives lengths of successive runs.

4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 1, 1, 2, 4, 2, 2, 4, 4, 2, 3, 1, 2, 2, 2, 2, 3, 3, 4, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 1, 1, 2, 4, 2, 2, 2, 2, 6

Offset: 1

Author

N. J. A. Sloane, Apr 29 2018

Keywords

• nonn

Examples

			The initial values of d(k) = A000005(k) for k = 1,2,3,... are
1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 2, 6, 2, 4, 4, 5, 2, 6, 2, 6, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 6, 4, 4, 4, 9, 2, 4, 4, 8, 2, 8, 2, 6, 6, 4, 2, 10, 3, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 7, 4, 8, 2, 6, 4, 8, 2, 12, 2, 4, 6, 6, 4, 8, 2, ...
Breaking this up into nondecreasing runs we get:
[1, 2, 2, 3], [2, 4], [2, 4], [3, 4], [2, 6], [2, 4, 4, 5], [2, 6], [2, 6], [4, 4], [2, 8], [3, 4, 4, 6], [2, 8], [2, 6], [4, 4, 4, 9], [2, 4, 4, 8], [2, 8], [2, 6, 6], [4], [2, 10], [3, 6], [4, 6], [2, 8], [4, 8], [4, 4], [2, 12], [2, 4, 6, 7], ...
whose successive lengths are
4,2,2,2,2,4,2,2,2,2,4,2,2,4,4,2,3,1,2,...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005.

A303578(m) gives value of n that starts the m-th run.

A284597(m) is the smallest number that starts a run of length m.

Extensions

More terms from Seiichi Manyama, Apr 29 2018