A262871 Sum of the squarefree numbers appearing among the smaller parts of the partitions of n into two parts.

0, 1, 1, 3, 3, 6, 6, 6, 6, 11, 11, 17, 17, 24, 24, 24, 24, 24, 24, 34, 34, 45, 45, 45, 45, 58, 58, 72, 72, 87, 87, 87, 87, 104, 104, 104, 104, 123, 123, 123, 123, 144, 144, 166, 166, 189, 189, 189, 189, 189, 189, 215, 215, 215, 215, 215, 215, 244, 244, 274

Offset

1,4

Links

Table of n, a(n) for n=1..60.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} i * mu(i)^2, where mu is the Möebius function (A008683).

a(n) = A262992(n) - A262870(n).

Example

a(5)=3; there are two partitions of 5 into two parts: (4,1) and (3,2). The sum of the smaller squarefree parts is 1+2=3. Thus a(5)=3.
a(6)=6; there are three partitions of 6 into two parts: (5,1), (4,2) and (3,3). All of the smaller parts are squarefree, so a(6) = 1+2+3 = 6.

Maple

with(numtheory): A262871:=n->add(i*mobius(i)^2, i=1..floor(n/2)): seq(A262871(n), n=1..100);

Mathematica

Table[Sum[i*MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 70}]

Prog

(PARI) a(n) = sum(i=1, n\2, i * moebius(i)^2); \\ Michel Marcus, Oct 04 2015
(PARI) a(n)=my(s); forsquarefree(k=1, n\2, s += k[1]); s \\ Charles R Greathouse IV, Jan 08 2018

Crossrefs

Cf. A008683, A071068, A261985, A262351, A262868, A262869, A262870, A262991, A262992.

Sequence in context: A271668 A370291 A072464 * A160745 A105676 A127739

Adjacent sequences: A262868 A262869 A262870 * A262872 A262873 A262874

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 03 2015

Status

approved