A181833 The number of positive integers <= n that are not strongly prime to n.

0, 0, 2, 3, 4, 4, 6, 5, 6, 7, 9, 5, 10, 7, 10, 11, 12, 6, 14, 7, 14, 15, 16, 5, 18, 13, 17, 13, 20, 7, 24, 9, 18, 19, 22, 15, 28, 10, 22, 19, 28, 9, 32, 9, 26, 27, 30, 5, 34, 17, 33, 25, 32, 7, 38, 23, 36, 29, 34, 5, 46

Offset

0,3

Comments

k is strongly prime to n iff k is relatively prime to n and k does not divide n-1.

a(n) = n - phi(n) + tau(n-1) if n > 0 and a(0) = 0.

Here phi(n) = A000010(n) and tau(n) = A000005(n).

Links

Table of n, a(n) for n=0..60.

Peter Luschny, Strong coprimality.

Example

a(11) = 11 - card({3,4,6,7,8,9}) = 5.

Maple

with(numtheory):
A181833 := n -> `if`(n=0, 0, n-phi(n)+tau(n-1));
A181833a := n -> n - A181830(n);

Mathematica

a[n_] := Select[Range[n], Not[CoprimeQ[#, n] && !Divisible[n-1, #]] &] // Length; a[1] = 0; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jun 28 2013 *)

Crossrefs

Cf. A181830, A181831, A181832, A181834, A181835, A181836, A051953.

Sequence in context: A091860 A333995 A301764 * A202650 A370829 A228286

Adjacent sequences: A181830 A181831 A181832 * A181834 A181835 A181836

Keyword

nonn

Author

Peter Luschny, Nov 17 2010

Status

approved