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A181833 The number of positive integers <= n that are not strongly prime to n. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 28 2013 *)

CROSSREFS

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

Sequence in context: A091860 A333995 A301764 * A202650 A228286 A158973

Adjacent sequences:  A181830 A181831 A181832 * A181834 A181835 A181836

KEYWORD

nonn

AUTHOR

Peter Luschny, Nov 17 2010

STATUS

approved

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Last modified January 17 16:45 EST 2021. Contains 340247 sequences. (Running on oeis4.)