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A199972 a(n) = the sum of GCQ_B(n, k) for 1 <= k <= n (see definition in comments). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 4 17:39 EDT 2022. Contains 355083 sequences. (Running on oeis4.)