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%I #36 Feb 11 2018 03:03:17
%S 0,1,2,5,3,8,11,18,18,18,23,34,28,41,48,63,63,80,80,99,89,110,121,144,
%T 144,144,157,157,143,172,187,218,218,251,268,303,303,340,359,398,398,
%U 439,460,503,481,481,504,551,551,551,551,602,576,629,629,684,684
%N Sum of the squarefree numbers appearing among the larger parts of the partitions of n into two parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor(n/2)} (n-i) * mu(n-i)^2, where mu is the Möebius function (A008683).
%F a(n) = A262992(n) - A262871(n).
%e a(4)=5; there are two partitions of 4 into two parts: (3,1) and (2,2). The sum of the larger squarefree parts is 3+2=5, thus a(4)=5.
%e a(5)=3; there are two partitions of 5 into two parts: (4,1) and (3,2). Of the larger parts, 3 is the only squarefree part, so a(5)=3.
%p with(numtheory): A262870:=n->add((n-i)*mobius(n-i)^2, i=1..floor(n/2)): seq(A262870(n), n=1..100);
%t Table[Sum[(n - i) MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 70}]
%o (PARI) a(n) = sum(i=1, n\2, (n-i) * moebius(n-i)^2); \\ _Michel Marcus_, Oct 04 2015
%o (PARI) a(n)=my(s); forsquarefree(k=(n+1)\2,n-1, s += k[1]); s \\ _Charles R Greathouse IV_, Jan 08 2018
%Y Cf. A008683, A071068, A261985, A262351, A262868, A262869, A262871, A262991, A262992.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Oct 03 2015
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