A199972 a(n) = the sum of GCQ_B(n, k) for 1 <= k <= n (see definition in comments).

0, 0, 4, 9, 19, 29, 41, 55, 71, 89, 109, 131, 155, 181, 209, 239, 271, 305, 341, 379, 419, 461, 505, 551, 599, 649, 701, 755, 811, 869, 929, 991, 1055, 1121, 1189, 1259, 1331, 1405, 1481, 1559, 1639, 1721, 1805, 1891, 1979, 2069

Offset

1,3

Comments

Definition of GCQ_B: The greatest common non-divisor of type B (GCQ_B) 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<=b common to a and b; GCQ_B(a, b) = 0 if no such c exists.

For b>=5 holds: GCQ_B(a, b) = b - 1 if a = b or a<= b-2, GCQ_B(a, b) = b - 2 if a = b-1.

Links

Table of n, a(n) for n=1..46.

Formula

a(n) = n*(n-1) - 1 for n>= 5.

Example

 For n = 4, a(4) = 9 because GCQ_B(4, 1) = 3, GCQ_B(4, 2) = 3, GCQ_B(4, 3) = 0, GCQ_B(4, 4) = 3 and sum of results is 9.
For n = 5, a(4) = 19 because GCQ_B(5, 1) = 4, GCQ_B(5, 2) = 4, GCQ_B(5, 3) = 4, GCQ_B(5, 4) = 3, GCQ_B(5, 5) = 4 and sum of results is 19.

Crossrefs

Cf.: A196443 (the sum of GCQ_A(n, k) for 1 <= k <= n).

Cf.: A199973 (the sum of LCQ_B(n, k) for 1 <= k <= n).

Cf.: A199971 (the sum of LCQ_A(n, k) for 1 <= k <= n).

Cf.: A199973 (the sum of LCQ_C(n, k) for 1 <= k <= n).

Sequence in context: A045278 A184723 A075649 * A327753 A100448 A059820

Adjacent sequences: A199969 A199970 A199971 * A199973 A199974 A199975

Keyword

nonn

Author

Jaroslav Krizek, Nov 26 2011

Status

approved