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A294096 Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime and smaller part squarefree. 1
0, 0, 1, 2, 1, 4, 3, 8, 5, 4, 0, 12, 10, 20, 11, 16, 5, 28, 22, 38, 18, 28, 14, 48, 34, 32, 7, 24, 26, 56, 30, 64, 47, 68, 23, 60, 34, 68, 54, 58, 21, 112, 85, 144, 59, 104, 62, 168, 82, 124, 61, 110, 83, 180, 81, 124, 71, 152, 62, 202, 91, 192, 132, 224, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..65.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor(n/2)} (n - 2i) * A008966(i) * A010051(n - i).

MATHEMATICA

Table[Sum[(n - 2 i) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[i]^2, {i, Floor[n/2]}], {n, 80}]

CROSSREFS

Cf. A010051, A008966, A294095.

Sequence in context: A179206 A331740 A074987 * A128280 A182177 A281878

Adjacent sequences:  A294093 A294094 A294095 * A294097 A294098 A294099

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Oct 22 2017

STATUS

approved

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Last modified September 22 17:39 EDT 2021. Contains 347607 sequences. (Running on oeis4.)