A375011 a(n) = A373738(n) - A008479(n).

0, 1, 1, 1, 1, 3, 1, 1, 1, 4, 1, 5, 1, 4, 3, 1, 1, 6, 1, 5, 3, 5, 1, 6, 1, 5, 1, 5, 1, 11, 1, 1, 4, 5, 3, 8, 1, 5, 4, 7, 1, 12, 1, 6, 5, 6, 1, 8, 1, 7, 4, 6, 1, 8, 3, 7, 4, 6, 1, 17, 1, 6, 5, 1, 3, 14, 1, 6, 4, 12, 1, 9, 1, 6, 6, 6, 3, 15, 1, 8, 1, 7, 1, 18, 3

Offset

1,6

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 2..2^20, ignoring a(1) = 0, with a color code where red indicates omega(n) = 2, gold omega(n) = 3, lime green = omega(n) = 4, spring green = omega(n) = 5, and blue = omega(n) = 6, where omega = A001221.

Formula

a(1) = 0; a(k) = 1 for k in A246655.

Mathematica

{0}~Join~Table[facs = FactorInteger[n][[All, 1]]; r = Times @@ facs;
  Floor[(1/PrimeNu[n]!)*Times @@ Map[Log[#, n] + 1 &, facs]] -
    Count[Range[n], _?(Times @@ FactorInteger[#][[All, 1]] == r &)], {n, 2, 120}]

Crossrefs

Cf. A001221, A008479, A246655, A372192, A373738.

Sequence in context: A270825 A364096 A348028 * A059619 A098950 A318873

Adjacent sequences: A375008 A375009 A375010 * A375012 A375013 A375014

Keyword

nonn

Author

Michael De Vlieger, Aug 14 2024

Status

approved