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

Author

Jaroslav Krizek, Nov 26 2011

Keywords

• nonn

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.

Examples

			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).

Formula

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