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A181830 The number of positive integers <= n that are strongly prime to n. 10
0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 1, 6, 2, 6, 4, 4, 4, 11, 4, 12, 6, 6, 6, 18, 6, 12, 9, 14, 8, 22, 6, 22, 14, 14, 12, 20, 8, 27, 16, 20, 12, 32, 10, 34, 18, 18, 16, 42, 14, 32, 17, 26, 20, 46, 16, 32, 20, 28, 24, 54, 14, 48, 28, 32, 26, 41, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

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

a(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..66.

Peter Luschny, Strong coprimality.

EXAMPLE

a(11) = card({1,2,3,4,5,6,7,8,9,10} - {1,2,5,10}) = card({3,4,6,7,8,9}) = 6.

MAPLE

with(numtheory):

A181830 := n -> `if`(n=0, 0, phi(n)-tau(n-1)):

StrongCoprimes := n -> select(k->igcd(k, n)=1, {$1..n}) minus divisors(n-1):

A181830a := n -> nops(StrongCoprimes(n)):

MATHEMATICA

a[0]=0; a[1]=1; a[n_ /; n > 1] := Select[Range[n], CoprimeQ[#, n] && !Divisible[n-1, #] &] // Length; Table[a[n], {n, 0, 66}] (* Jean-Fran├žois Alcover, Jun 26 2013 *)

PROG

(Pari) a(n)=if(n<2, n, eulerphi(n)-numdiv(n-1));

for (i=0, 66, print1(a(i), ", ")) \\ Michel Marcus, May 22 2017

CROSSREFS

Cf. A181831, A181832, A181833, A181834, A181835, A181836, A000010, A000005.

Sequence in context: A114293 A285183 A255399 * A086612 A128207 A180958

Adjacent sequences:  A181827 A181828 A181829 * A181831 A181832 A181833

KEYWORD

nonn,easy

AUTHOR

Peter Luschny, Nov 17 2010

STATUS

approved

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Last modified June 23 19:51 EDT 2017. Contains 288675 sequences.