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

1,3

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.

Links

Table of n, a(n) for n=1..50.

Example

 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).

Sequence in context: A368680 A231365 A024816 * A007316 A163905 A353653

Adjacent sequences: A196440 A196441 A196442 * A196444 A196445 A196446

Keyword

nonn

Author

Jaroslav Krizek, Nov 26 2011

Status

approved