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 A196437 a(n) = the number of numbers k <= n such that GCQ_A(n, k) = LCQ_A(n, k) = 0 (see definition in comments). 8
 1, 2, 2, 3, 2, 4, 2, 3, 3, 3, 2, 5, 2, 3, 3, 3, 2, 4, 2, 4, 3, 3, 2, 5, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 5, 2, 3, 3, 4, 2, 4, 2, 3, 3, 3, 2, 5, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 7, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 5, 2, 3, 3, 3, 2, 4, 2, 4, 3, 3, 2, 5, 2, 3, 3, 3, 2, 4, 2, 3, 3, 3, 2, 5, 2, 3, 3, 4, 2, 4, 2, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Definition of GCQ_A: The greatest common non-divisor of type A (GCQ_A) of two positive integers a and b (a<=b) is the largest positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; GCQ_A(a, b) = 0 if no such c exists. GCQ_A(1, b) = GCQ_A(2, b) = 0 for b >=1. GCQ_A(a, b) = 0 or >= 2. Definition of LCQ_A: The least common non-divisor of type A (LCQ_A) of two positive integers a and b (a<=b) is the least positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; LCQ_A(a, b) = 0 if no such c exists. LCQ_A(1, b) = LCQ_A(2, b) = 0 for b >=1. LCQ_A(a, b) = 0 or >= 2. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = n - A196438(n). EXAMPLE For n = 6, a(6) = 4 because there are 4 cases with GCQ_A(6, k) = 0: GCQ_A(6, 1) = 0, GCQ_A(6, 2) = 0, GCQ_A(6, 3) = 0, GCQ_A(6, 4) = 0, GCQ_A(6, 5) = 4, GCQ_A(6, 6) = 5. Also there are 4 cases with LCQ_A(6, k) = 0: LCQ_A(6, 1) = 0, LCQ_A(6, 2) = 0, LCQ_A(6, 3) = 0, LCQ_A(6, 4) = 0, LCQ_A(6, 5) = 4, LCQ_A(6, 6) = 4. PROG (PARI) GCQ_A(a, b) = { forstep(m=min(a, b)-1, 2, -1, if(a%m && b%m, return(m))); 0; }; A196438(n) = sum(i=3, n, GCQ_A(i, n)>=2); A196437(n) = (n - A196438(n)); \\ Antti Karttunen, Mar 20 2018, based on Charles R Greathouse IV's Aug 26 2017 PARI-program in A196438. CROSSREFS Cf. A196438, A196439, A196440, A196441, A196442, A196443, A196444. Sequence in context: A083902 A205562 A217984 * A106491 A073184 A073182 Adjacent sequences: A196434 A196435 A196436 * A196438 A196439 A196440 KEYWORD nonn AUTHOR Jaroslav Krizek, Nov 26 2011 EXTENSIONS More terms from Antti Karttunen, Mar 20 2018 STATUS approved

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Last modified June 15 09:53 EDT 2024. Contains 373407 sequences. (Running on oeis4.)