A262870 Sum of the squarefree numbers appearing among the larger parts of the partitions of n into two parts.

0, 1, 2, 5, 3, 8, 11, 18, 18, 18, 23, 34, 28, 41, 48, 63, 63, 80, 80, 99, 89, 110, 121, 144, 144, 144, 157, 157, 143, 172, 187, 218, 218, 251, 268, 303, 303, 340, 359, 398, 398, 439, 460, 503, 481, 481, 504, 551, 551, 551, 551, 602, 576, 629, 629, 684, 684

Offset

1,3

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to partitions

Formula

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

a(n) = A262992(n) - A262871(n).

Example

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.
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.

Maple

with(numtheory): A262870:=n->add((n-i)*mobius(n-i)^2, i=1..floor(n/2)): seq(A262870(n), n=1..100);

Mathematica

Table[Sum[(n - i) MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 70}]

Prog

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

Crossrefs

Cf. A008683, A071068, A261985, A262351, A262868, A262869, A262871, A262991, A262992.

Sequence in context: A302054 A081146 A261927 * A294210 A244418 A082652

Adjacent sequences: A262867 A262868 A262869 * A262871 A262872 A262873

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 03 2015

Status

approved