

A262871


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


7



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
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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: A175520 A271668 A072464 * A160745 A105676 A127739
Adjacent sequences: A262868 A262869 A262870 * A262872 A262873 A262874


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Oct 03 2015


STATUS

approved



