The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
Sequence in context: A083902 A205562 A217984 * A106491 A073184 A073182
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Nov 26 2011
EXTENSIONS
More terms from Antti Karttunen, Mar 20 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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