A303577 - OEIS

%I #23 Jun 25 2018 22:58:25

%S 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,

%T 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,

%U 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

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

%H Seiichi Manyama, <a href="/A303577/b303577.txt">Table of n, a(n) for n = 1..10000</a>

%e The initial values of d(k) = A000005(k) for k = 1,2,3,... are

%e 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, ...

%e Breaking this up into nondecreasing runs we get:

%e [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], ...

%e whose successive lengths are

%e 4,2,2,2,2,4,2,2,2,2,4,2,2,4,4,2,3,1,2,...

%Y Cf. A000005.

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

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

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Apr 29 2018

%E More terms from _Seiichi Manyama_, Apr 29 2018