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A280534 Number of partitions of n into two parts with the smaller part prime and the larger part squarefree. 2
0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 1, 5, 3, 5, 2, 5, 2, 3, 2, 4, 4, 5, 3, 6, 4, 5, 4, 7, 5, 6, 4, 6, 5, 7, 3, 7, 6, 6, 3, 6, 5, 7, 3, 6, 4, 8, 4, 9, 4, 8, 4, 10, 5, 8, 3, 8, 6, 9, 4, 10, 5, 9, 6, 10, 5, 9, 5, 9, 6, 9, 5, 12, 6, 8, 6, 11, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Number of distinct rectangles with squarefree length and prime width such that L + W = n, W <= L. For example, a(16) = 3; the rectangles are 2 X 14, 3 X 13 and 5 X 11. - Wesley Ivan Hurt, Nov 04 2017

LINKS

Table of n, a(n) for n=1..89.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor(n/2)} A010051(i) * mu(n-i)^2, where mu is the Möbius function (A008683).

MAPLE

with(numtheory): A280534:=n->add(mobius(n-i)^2*(pi(i)-pi(i-1)), i=1..floor(n/2)): seq(A280534(n), n=1..100); # Wesley Ivan Hurt, Jan 04 2017

MATHEMATICA

Table[Sum[MoebiusMu[n - k]^2 * (PrimePi[k] - PrimePi[k - 1]), {k, 1, Floor[n/2]}], {n, 1, 50}] (* G. C. Greubel, Jan 05 2017 *)

PROG

(PARI) for(n=1, 50, print1(sum(k=1, floor(n/2), isprime(k)*(moebius(n-k))^2), ", ")) \\ G. C. Greubel, Jan 05 2017

CROSSREFS

Cf. A008683, A010051, A280535.

Sequence in context: A046799 A319506 A037809 * A129451 A097195 A274138

Adjacent sequences:  A280531 A280532 A280533 * A280535 A280536 A280537

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Jan 04 2017

STATUS

approved

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Last modified July 5 01:22 EDT 2020. Contains 335457 sequences. (Running on oeis4.)