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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 December 4 15:36 EST 2021. Contains 349526 sequences. (Running on oeis4.)