cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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

Views

Author

Alonso del Arte, Jan 03 2005

Keywords

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

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

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Dec 30 2004

Keywords

Links

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

A100766 Numbers for which the values of the Moebius function (A008683) and the Mertens function (A002321) are both 0.

Original entry on oeis.org

40, 150, 160, 164, 232, 236, 332, 333, 356, 363, 364, 404, 405, 408, 414, 420, 423, 424, 425, 428, 608, 636, 637, 796, 812, 824, 825, 850, 884, 896, 904, 916, 920, 1014, 1220, 1256, 1280, 1292, 1300, 1336, 1492, 1519, 1520, 1521, 1524, 1525, 1528, 1532, 1544
Offset: 1

Views

Author

Alonso del Arte, Jan 03 2005

Keywords

Comments

This sequence is a subset of A100306, numbers for which the values of the Moebius function and the Mertens function agree and, in a different way, a subset of A028442, zeros of the Mertens function. There are no prime numbers in this sequence.
Numbers k such that k-1 and k are consecutive zeros of the Mertens function. - Amiram Eldar, Jun 13 2020

Links

Crossrefs

Cf. A100306, A100765, A100767.

Programs

  • Mathematica
    (* If not already defined *) If[Names["Mertens"] == {}, Mertens[x_] := Plus @@ MoebiusMu[Range[1, x]]]; Select[Range[2500], MoebiusMu[ # ] == 0 && Mertens[ # ] == 0 &]

Extensions

Offset corrected by Donovan Johnson, Jun 19 2012
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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