

A196439


a(n) = the sum of numbers k <= n such that GCQ_A(n, k) = LCQ_A(n, k) = 0 (see definition in comments).


8



1, 3, 3, 6, 3, 10, 3, 6, 7, 6, 3, 15, 3, 6, 7, 6, 3, 10, 3, 12, 7, 6, 3, 15, 3, 6, 7, 6, 3, 10, 3, 6, 7, 6, 3, 15, 3, 6, 7, 12, 3, 10, 3, 6, 7, 6, 3, 15, 3, 6, 7, 6, 3, 10, 3, 6, 7, 6, 3, 28, 3, 6, 7, 6, 3, 10, 3, 6, 7, 6, 3, 15, 3, 6, 7, 6, 3, 10, 3, 12, 7, 6, 3, 15, 3, 6, 7, 6, 3, 10, 3, 6, 7, 6, 3, 15, 3, 6, 7, 12, 3, 10, 3, 6, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Definition of GCQ_A: The greatest common nondivisor of type A (GCQ_A) of two positive integers a and b (a<=b) is the largest positive nondivisor 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 nondivisor of type A (LCQ_A) of two positive integers a and b (a<=b) is the least positive nondivisor 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



EXAMPLE

For n = 6, a(6) = 10 because there are 4 cases k (k = 1, 2, 3, 4) 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. Sum of such numbers k is 10.
Also there are 4 same cases k 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; }; \\ From PARIprogram in A196438.
A196440(n) = sum(k=1, n, (2<=GCQ_A(n, k))*k);


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



