A261985 Sum of the smaller parts of the partitions of n into two squarefree parts.
0, 1, 1, 3, 2, 4, 3, 6, 5, 8, 6, 14, 11, 11, 8, 17, 18, 16, 13, 32, 25, 27, 19, 39, 32, 39, 35, 58, 40, 47, 32, 61, 47, 65, 41, 93, 58, 67, 54, 95, 73, 80, 89, 130, 109, 94, 87, 142, 110, 106, 102, 203, 129, 130, 115, 189, 148, 151, 137, 232, 170, 165, 169
Offset: 1
Examples
a(4)=3; there are two partitions of 4 into two squarefree parts: (3,1) and (2,2). The sum of the smaller parts of these partitions is 1+2=3. a(6)=4; there are two partitions of 6 into two squarefree parts: (5,1) and (3,3). The sum of the smaller parts is 1+3=4.
Links
Programs
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Maple
with(numtheory): A261985:=n->add(i*mobius(i)^2*mobius(n-i)^2, i=1..floor(n/2)): seq(A261985(n), n=1..100);
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Mathematica
Table[Sum[i*MoebiusMu[i]^2*MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 100}] -
PARI
a(n) = sum(i=1, n\2, i*moebius(i)^2*moebius(n-i)^2); \\ Altug Alkan, Jan 01 2018
Formula
a(n) = Sum_{i=1..floor(n/2)} (i * mu(i)^2 * mu(n-i)^2), where mu is the Moebius function (A008683).
a(n) = A303221(n)/n. - Wesley Ivan Hurt, Jan 05 2024
Comments