A309479 - OEIS

A309479

Sum of the squarefree parts of the partitions of n into 4 parts.

0, 0, 0, 0, 4, 5, 12, 17, 36, 46, 74, 93, 135, 169, 232, 278, 384, 462, 587, 702, 881, 1009, 1250, 1432, 1728, 1976, 2338, 2637, 3091, 3481, 3987, 4466, 5114, 5658, 6420, 7091, 7967, 8775, 9813, 10729, 11983, 13089, 14467, 15771, 17422, 18890, 20784, 22504

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (i * mu(i)^2 + j * mu(j)^2 + k * mu(k)^2 + (n-i-j-k) * mu(n-i-j-k)^2), where mu is the Möbius function (A008683).

EXAMPLE

Figure 1: The partitions of n into 4 parts for n = 8, 9, ..

1+1+1+9

1+1+2+8

1+1+3+7

1+1+4+6

1+1+1+8 1+1+5+5

1+1+2+7 1+2+2+7

1+1+1+7 1+1+3+6 1+2+3+6

1+1+2+6 1+1+4+5 1+2+4+5

1+1+3+5 1+2+2+6 1+3+3+5

1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4

1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6

1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5

1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4

1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4

2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3

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n | 8 9 10 11 12 ...

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a(n) | 36 46 74 93 135 ...

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- Wesley Ivan Hurt, Sep 07 2019

MATHEMATICA

Table[Sum[Sum[Sum[(i*MoebiusMu[i]^2 + j*MoebiusMu[j]^2 + k*MoebiusMu[k]^2 + (n - i - j - k)*MoebiusMu[n - i - j - k]^2), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]

CROSSREFS

Cf. A008683, A309456, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.

Sequence in context: A261692 A131328 A054451 * A352720 A369697 A308775

Adjacent sequences: A309476 A309477 A309478 * A309480 A309481 A309482

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 04 2019

STATUS

approved