A137947 a(n) = k: k is smallest integer > 1 such that sign(d(1)-d(2)) = sign(d(k)-d(k+1)), sign(d(2)-d(3)) = sign(d(k+1)-d(k+2)),...,sign(d(n)-d(n+1)) = sign(d(k+n-1)-d(k+n)), where sign is (-,0,+) and d(m) = the number of positive divisors of m.

3, 13, 13, 13, 13, 13, 13, 13, 121, 121, 121, 121, 985, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489, 10489

Offset

1,1

Comments

a(33) > 2300000 if it exists. - R. J. Mathar, Apr 21 2008

Links

Table of n, a(n) for n=1..32.

Maple

A000005 := proc(n) numtheory[tau](n) ; end: A137947 := proc(n) local k, o, works ; for k from 2 do works := true ; for o from 1 to n do if signum(A000005(o)-A000005(o+1)) <> signum(A000005(k+o-1)-A000005(k+o)) then works := false ; break ; fi ; od: if works then RETURN(k) ; fi ; od: end: for n from 1 do print(n, A137947(n)) ; od: # R. J. Mathar, Apr 21 2008

Crossrefs

Cf. A000005.

Sequence in context: A273076 A272825 A054767 * A168437 A076747 A198452

Adjacent sequences: A137944 A137945 A137946 * A137948 A137949 A137950

Keyword

nonn

Author

Leroy Quet, Feb 24 2008, Mar 09 2008

Extensions

More terms from R. J. Mathar, Apr 21 2008

Status

approved