

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 iff k is relatively prime to n and k does not divide n1.
a(n) = phi(n)  tau(n1) 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(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, eulerphi(n)numdiv(n), 0) \\ Charles R Greathouse IV, Jun 26 2013


CROSSREFS

Cf. A181831, A181832, A181833, A181834, A181835, A181836, A000010, A000005.
Sequence in context: A184242 A109978 A114293 * A086612 A128207 A180958
Adjacent sequences: A181827 A181828 A181829 * A181831 A181832 A181833


KEYWORD

nonn,easy


AUTHOR

Peter Luschny, Nov 17 2010


STATUS

approved



