

A181830


The number of positive integers <= n that are strongly prime to n.


13



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
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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(n1) if n > 0 and a(0) = 0. Here phi(n) = A000010(n) and tau(n) = A000005(n).
It is conjectured (see Scroggs link) that a(n) is also the number of cardboard braids that work with n slots.  Matthew Scroggs, Sep 23 2017
a(n) is odd if and only if n is in A002522 but n <> 2.  Robert Israel, Jun 20 2018


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
Peter Luschny, Strong coprimality
Matthew Scroggs, Braiding, pt. 2. Two results and a conjecture


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(n1)):
StrongCoprimes := n > select(k > igcd(k, n)=1, {$1..n}) minus divisors(n1):
A181830a := n > nops(StrongCoprimes(n)):


MATHEMATICA

a[0]=0; a[1]=1; a[n_ /; n > 1] := Select[Range[n], CoprimeQ[#, n] && !Divisible[n1, #] &] // Length; Table[a[n], {n, 0, 66}] (* JeanFrançois Alcover, Jun 26 2013 *)


PROG

(Pari) a(n)=if(n<2, n, eulerphi(n)numdiv(n1));
for (i=0, 66, print1(a(i), ", ")) \\ Michel Marcus, May 22 2017


CROSSREFS

Cf. A000005, A000010, A002522, A181831, A181832, A181833, A181834, A181835, A181836.
Cf. A050384.
Sequence in context: A295691 A285183 A255399 * A086612 A128207 A306707
Adjacent sequences: A181827 A181828 A181829 * A181831 A181832 A181833


KEYWORD

nonn,easy


AUTHOR

Peter Luschny, Nov 17 2010


STATUS

approved



