A294342 Numbers k at which the ratio (number of squares in the multiplicative group modulo k)/k reaches a new minimum.

1, 2, 3, 4, 6, 8, 12, 24, 60, 120, 420, 840, 4620, 9240, 60060, 120120, 1021020, 2042040, 19399380, 38798760, 446185740, 892371480

Offset: 1

Author

Jon E. Schoenfield, Oct 28 2017

Keywords

• nonn
• more

Comments

I.e., numbers k such that A046073(k)/k < A046073(j)/j for all j < k.

Appears to be just the union of 2*A002110, 4*A002110, and {1,3,6}. - Don Reble, Nov 26 2017

Examples

			     k    A046073(k)              A046073(k)/k
  ======= ========== ========================================
        1       1       1/1       =   1      = 1.000000000
        2       1       1/2       =  1/2     = 0.500000000
        3       1       1/3       =  1/3     = 0.333333333...
        4       1       1/4       =  1/4     = 0.250000000
        6       1       1/6       =  1/6     = 0.166666666...
        8       1       1/8       =  1/8     = 0.125000000
       12       1       1/12      =  1/12    = 0.083333333...
       24       1       1/24      =  1/24    = 0.041666666...
       60       2       2/60      =  1/30    = 0.033333333...
      120       2       2/120     =  1/60    = 0.016666666...
      420       6       6/420     =  1/70    = 0.014285714...
      840       6       6/840     =  1/140   = 0.007142857...
     4620      30      30/4620    =  1/154   = 0.006493506...
     9240      30      30/9240    =  1/308   = 0.003246753...
    60060     180     180/60060   =  3/1001  = 0.002997002...
   120120     180     180/120120  =  3/2002  = 0.001498501...
  1021020    1440    1440/1021020 = 24/17017 = 0.001410354...
  2042040    1440    1440/2042040 = 12/17017 = 0.000705177...
		

Crossrefs

Cf. A046073.

Programs

PARI

m=oo;for(k=1,oo, m > A046073(k)/k||next;print1(k",");m=A046073(k)/k) \\ M. F. Hasler, Nov 27 2017

Extensions

Terms a(19) .. a(22) from Joerg Arndt, Dec 28 2017