A114180 Numbers n with mu(n) = mu(n+1) = mu(n+2).

29, 33, 41, 48, 85, 93, 98, 101, 124, 137, 141, 201, 213, 217, 229, 242, 243, 281, 301, 342, 350, 393, 423, 429, 433, 445, 475, 548, 603, 617, 633, 641, 645, 697, 724, 741, 774, 821, 844, 845, 846, 869, 921, 969, 1021, 1024, 1041, 1085, 1129, 1137, 1189

Offset: 1

Author

Franklin T. Adams-Watters, Feb 03 2006

Keywords

• nonn

Comments

Any sequence of 4 or more consecutive numbers with the same value for mu must all have mu(n)=0 (n divisible by a proper square) since at least one of every 4 consecutive numbers is divisible by 4.

A261890(a(n)) = 0. - Reinhard Zumkeller, Sep 05 2015

Examples

			mu(n)=1 for 33,34,35; 85,86,87; 93,94,95; ...
mu(n)=-1 for 29,30,31; 41,42,43; 101,102,103; ...
mu(n)=0 for 48,49,50; 98,99,100; 124,125,126; ...
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Union of A070258, A063838 and A070268. Cf. A008683, A070284.

Cf. A261890.

Programs

Haskell

a114180 n = a114180_list !! (n-1)
a114180_list = filter ((== 0) . a261890) [1..]
-- Reinhard Zumkeller, Sep 05 2015

Mathematica

SequencePosition[MoebiusMu[Range[1200]],{x_,x_,x_}][[;;,1]] (* Harvey P. Dale, Jul 23 2023 *)