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A294145 Sum of the smaller parts of the partitions of n into two parts with larger part squarefree. 2
0, 1, 1, 3, 2, 4, 3, 6, 9, 12, 10, 14, 11, 15, 12, 17, 22, 28, 34, 41, 37, 44, 40, 48, 56, 64, 59, 67, 60, 68, 61, 70, 79, 89, 82, 93, 104, 116, 109, 122, 135, 149, 142, 157, 149, 163, 154, 169, 184, 199, 214, 230, 219, 235, 251, 268, 285, 303, 292, 311, 299 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..61.

Index entries for sequences related to partitions

FORMULA

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

MATHEMATICA

Table[Sum[i*MoebiusMu[n - i]^2, {i, Floor[n/2]}], {n, 80}]

Table[Total[Select[IntegerPartitions[n, {2}], SquareFreeQ[#[[1]]]&][[All, 2]]], {n, 70}] (* Harvey P. Dale, Dec 26 2020 *)

CROSSREFS

Cf. A008683, A008966, A294146.

Sequence in context: A026923 A058708 A141731 * A024856 A147598 A023869

Adjacent sequences:  A294142 A294143 A294144 * A294146 A294147 A294148

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 23 2017

STATUS

approved

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Last modified January 24 09:58 EST 2022. Contains 350534 sequences. (Running on oeis4.)