A100306 Numbers for which the values of the Moebius function (A008683) and the Mertens function (A002321) agree.

1, 3, 40, 41, 59, 66, 94, 102, 146, 150, 151, 160, 161, 164, 165, 167, 215, 232, 233, 236, 237, 239, 255, 330, 332, 333, 334, 354, 356, 357, 359, 363, 364, 365, 367, 394, 402, 404, 405, 406, 408, 409, 414, 415, 420, 421, 423, 424, 425, 426, 428, 429, 538, 542

Offset: 1

Author

N. J. A. Sloane, Dec 30 2004

Keywords

• nonn

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• PrimeFan, Esoteric Integer Sequences
• PrimeFan, Esoteric Integer Sequences [Cached copy]

Crossrefs

Cf. A100765, A100766, A100767.

Programs

Maple

with(numtheory): p:=proc(n) if mobius(n)=sum(mobius(k),k=1..n) then n else fi end: seq(p(n),n=1..700); # Emeric Deutsch, Feb 14 2005

Mathematica

Select[Range[500], Plus @@ MoebiusMu[Range[#]] == MoebiusMu[#] &] (* Carl Najafi, Aug 17 2011 *)

PARI

s=0; for(n=1,1e4, s+=t=moebius(n); if(t==s, print1(n", "))) \\ Charles R Greathouse IV, Jan 28 2014

Extensions

More terms from Emeric Deutsch, Feb 14 2005