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 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 (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). 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(n-1)): StrongCoprimes := n -> select(k -> igcd(k, n)=1, {\$1..n}) minus divisors(n-1): A181830a := n -> nops(StrongCoprimes(n)): MATHEMATICA a=0; a=1; a[n_ /; n > 1] := Select[Range[n], CoprimeQ[#, n] && !Divisible[n-1, #] &] // Length; Table[a[n], {n, 0, 66}] (* Jean-François 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. 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

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Last modified May 28 01:48 EDT 2020. Contains 334671 sequences. (Running on oeis4.)