The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A133295 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A133295

Smallest squarefree k such that the first n nonzero values of mu(j), j>=k, are all equal (mu is the Moebius function).
(history; published version)

#10 by Alois P. Heinz at Fri Aug 30 08:13:28 EDT 2019

STATUS

reviewed

approved

#9 by Michel Marcus at Fri Aug 30 04:19:15 EDT 2019

STATUS

proposed

reviewed

#8 by Michel Marcus at Fri Aug 30 04:19:12 EDT 2019

STATUS

editing

proposed

#7 by Michel Marcus at Fri Aug 30 04:19:09 EDT 2019

EXAMPLE

a(6)=201 because the first occurrence of 6 consecutive squarefree numbers with numbers of prime divisors having the same parity is 201, 202, 203, 205, 206, 209.

STATUS

reviewed

editing

#6 by Joerg Arndt at Fri Aug 30 04:16:27 EDT 2019

STATUS

proposed

reviewed

#5 by Amiram Eldar at Fri Aug 30 03:58:28 EDT 2019

STATUS

editing

proposed

#4 by Amiram Eldar at Fri Aug 30 03:38:38 EDT 2019

LINKS

Amiram Eldar, <a href="/A133295/b133295.txt">Table of n, a(n) for n = 1..37</a>

#3 by Amiram Eldar at Fri Aug 30 03:38:18 EDT 2019

DATA

1, 2, 2, 91, 97, 201, 201, 598, 2683, 2683, 2683, 3090, 3090, 38401, 38401, 41226, 293037, 293037, 294574, 2156849, 4819826, 8812154, 10309514, 10309514, 10309514, 39479386, 476531349, 768912879, 1654065545, 5332819918, 8974545041, 16907435569, 17785220641

MATHEMATICA

f[n_] := Module[{c = 0, m = MoebiusMu[n]}, If[m == 0, Return[0]]; nn = n; mm = m; While[mm == 0 || mm == m, If[mm != 0, c++]; nn++; mm = MoebiusMu[nn]]; c]; mx = 19; v = Table[0, {mx}]; count = 0; Do[f1 = f[n]; Do[If[v[[j]] == 0, v[[j]] = n; count++], {j, 1, f1}]; If[count == mx, Break[]], {n, 1, 10^6}]; v (* Amiram Eldar, Aug 30 2019 *)

CROSSREFS

Cf. A005117, A008683.

EXTENSIONS

More terms from Amiram Eldar, Aug 30 2019

STATUS

approved

editing

#2 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Smallest square-free squarefree k such that the first n nonzero values of mu(j), j>=k, are all equal (mu is the Moebius function).

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

NAME

Smallest square-free k such that the first n nonzero values of mu(j), j>=k, are all equal (mu is the Moebius function).

DATA

1, 2, 2, 91, 97, 201, 201

OFFSET

1,2

EXAMPLE

a(6)=201 because the first occurrence of 6 consecutive squarefree numbers with numbers of prime divisors having the same parity is 201, 202, 203, 205, 206, 209

KEYWORD

nonn,new

AUTHOR

Michel Balazard (balazard(AT)math.u-bordeaux1.fr), Oct 17 2007, Oct 19 2007

STATUS

approved