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A302538 Number of partitions of n into two parts (p,q) with p <= q such that p is squarefree and q is semiprime. 1
0, 0, 0, 0, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 3, 4, 3, 1, 1, 3, 2, 2, 2, 3, 3, 3, 5, 6, 3, 2, 3, 4, 2, 2, 5, 7, 4, 4, 6, 8, 6, 4, 4, 6, 5, 4, 5, 7, 6, 4, 4, 8, 5, 5, 4, 8, 6, 5, 6, 8, 7, 6, 7, 9, 8, 6, 6, 12, 7, 8, 6, 11, 5, 5, 8, 9, 7, 6, 9, 9, 6, 5, 7, 11, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Table of n, a(n) for n=1..85.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} mu(i)^2 * [Omega(n-i) == 2], where [] is the Iverson bracket, mu = A008683 and Omega = A001222.

MATHEMATICA

Table[Sum[MoebiusMu[i]^2 KroneckerDelta[PrimeOmega[n - i], 2], {i, Floor[n/2]}], {n, 100}]

CROSSREFS

Cf. A001222, A008683, A303119.

Sequence in context: A072906 A239062 A201160 * A228428 A321915 A321748

Adjacent sequences:  A302535 A302536 A302537 * A302539 A302540 A302541

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 18 2018

STATUS

approved

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Last modified December 10 12:33 EST 2018. Contains 318047 sequences. (Running on oeis4.)