A199974 -id:A199974 - cp's OEIS frontend

A199973 a(n) = the sum of LCQ_B(n, k) for 1 <= k <= n (see definition in comments).

0, 0, 4, 9, 12, 25, 18, 28, 28, 33, 28, 64, 35, 47, 51, 59, 45, 76, 51, 81, 68, 74, 61, 128, 72, 88, 87, 103, 78, 145, 84, 119, 107, 114, 101, 195, 101, 129, 126, 166

Offset: 1

Jaroslav Krizek, Nov 26 2011

nonn

Definition of LCQ_B: The least common non-divisor of type B (LCQ_B) of two positive integers a and b (a<=b) is the least positive non-divisor q of numbers a and b such that 1<=q<=b common to a and b; LCQ_B(a, b) = 0 if no such c exists.

LCQ_B(a, b) = 0 or >= 2.

Cf.: A196443 (the sum of GCQ_A(n, k) for 1 <= k <= n).
Cf.: A199972 (the sum of GCQ_B(n, k) for 1 <= k <= n).
Cf.: A199971 (the sum of LCQ_A(n, k) for 1 <= k <= n).
Cf.: A199974 (the sum of LCQ_C(n, k) for 1 <= k <= n).

For n = 6, a(6) = 9 because LCQ_B(6, 1) = 4, LCQ_B(6, 2) = 4, LCQ_B(6, 3) = 4, LCQ_B(6, 4) = 5, LCQ_B(6, 5) = 4, LCQ_B(6, 6) = 4. Sum of results is 25.

A199971 a(n) = the sum of LCQ_A(n, k) for 1 <= k <= n (see definition in comments).

Original entry on oeis.org

0, 0, 2, 3, 7, 8, 13, 17, 17, 23, 23, 37, 30, 37, 39, 48, 40, 59, 46, 62, 57, 64, 56, 101, 67, 78, 76, 92, 73, 126, 79, 108, 96, 104, 96, 168, 96, 119, 115, 147

Offset: 1

Jaroslav Krizek, Nov 26 2011

nonn

Definition of LCQ_A: The least common non-divisor of type A (LCQ_A) of two positive integers a and b (a<=b) is the least positive non-divisor q of numbers a and b such that 1<=q<=a common to a and b; LCQ_A(a, b) = 0, if no such c exists.

LCQ_A(1, b) = LCQ_A(2, b) = 0 for b >=1. LCQ_A(a, b) = 0 or >= 2.

			For n = 6, a(6) = 9 because LCQ_A(6, 1) = 0, LCQ_A(6, 2) = 0, LCQ_A(6, 3) = 0, LCQ_A(6, 4) = 0, LCQ_A(6, 5) = 4, LCQ_A(6, 6) = 4. Sum of results is 8.

Cf.: A196443 (the sum of GCQ_A(n, k) for 1 <= k <= n).
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).
Cf.: A199974 (the sum of LCQ_C(n, k) for 1 <= k <= n).

cp's OEIS Frontend

A199973 a(n) = the sum of LCQ_B(n, k) for 1 <= k <= n (see definition in comments).

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