login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A309484 Sum of the squarefree parts of the partitions of n into 8 parts. 0
0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 20, 29, 56, 83, 138, 193, 299, 408, 594, 789, 1115, 1462, 1977, 2551, 3382, 4279, 5550, 6948, 8856, 10970, 13742, 16841, 20832, 25303, 30892, 37180, 44972, 53652, 64276, 76108, 90424, 106352, 125353, 146501, 171544, 199318 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..45.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (i * mu(i)^2 + j * mu(j)^2 + k * mu(k)^2 + l * mu(l)^2 + m * mu(m)^2 + o * mu(o)^2 + p * mu(p)^2 + (n-i-j-k-l-m-o-p) * mu(n-i-j-k-l-m-o-p)^2), where mu is the Möbius function (A008683).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(i * MoebiusMu[i]^2 + j * MoebiusMu[j]^2 + k * MoebiusMu[k]^2 + l * MoebiusMu[l]^2 + m * MoebiusMu[m]^2 + o * MoebiusMu[o]^2 + p * MoebiusMu[p]^2 + (n - i - j - k - l - m - o - p) * MoebiusMu[n - i - j - k - l - m - o - p]^2), {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 100}]

CROSSREFS

Cf. A008683, A309461.

Sequence in context: A281225 A071869 A326444 * A308989 A048124 A322637

Adjacent sequences:  A309481 A309482 A309483 * A309485 A309486 A309487

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 04 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 20 19:05 EDT 2019. Contains 327246 sequences. (Running on oeis4.)