A196443 a(n) = the sum of GCQ_A(n, k) for 1 <= k <= n (see definition in comments).

0, 0, 2, 3, 9, 9, 20, 24, 32, 41, 54, 55, 77, 87, 100, 115, 135, 145, 170, 180, 205, 227, 252, 263, 298, 321, 346, 372, 405, 424, 464, 490, 523, 557, 592, 616, 665, 699, 736, 768, 819, 850, 902, 940, 983, 1031, 1080, 1113, 1174, 1219

Offset: 1

Author

Jaroslav Krizek, Nov 26 2011

Keywords

• nonn

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.

Examples

			 For n = 6, a(6) = 9 because 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 results is 9.
		

Crossrefs

Cf. A196437, A196438, A196439, A196440, A196441, A196442, A196444, A018804.

Cf. A199972 (the sum of GCQ_B(n, k) for 1<= k <= n).

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