A100765 Numbers for which the values of the Moebius function (A008683) and the Mertens function (A002321) are both -1.

3, 41, 59, 66, 102, 151, 165, 167, 233, 239, 255, 354, 357, 359, 367, 402, 406, 409, 421, 426, 429, 609, 638, 782, 786, 797, 826, 854, 885, 887, 890, 894, 897, 907, 911, 1015, 1019, 1221, 1259, 1281, 1283, 1298, 1301, 1303, 1307, 1319, 1327, 1493, 1526, 1533

Offset: 1

Author

Alonso del Arte, Jan 03 2005

Keywords

• nonn

Comments

This sequence is a subsequence of A100306, Numbers for which the values of the Moebius function and the Mertens function agree.

Examples

			102 is in the sequence because it is a sphenic number (exactly 3 distinct prime factors, A007304) number, so the Mobius function yields -1 and the sum of that value and the previous Mobius values (the Mertens function) is also -1.
		

Links

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

Crossrefs

Cf. A100306, A100766, A100767.

Programs

Mathematica

(* If not already defined *) If[Names["Mertens"] == {}, Mertens[x_] := Plus @@ MoebiusMu[Range[1, x]]]; Select[Range[2500], MoebiusMu[ # ] == -1 && Mertens[ # ] == -1 &]

Extensions

Offset corrected by Donovan Johnson, Jun 19 2012