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A302643 Number of partitions of n into two parts such that the positive difference of the parts is a squarefree semiprime. 2
0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 0, 3, 1, 3, 1, 3, 1, 3, 2, 4, 2, 4, 2, 5, 2, 5, 2, 5, 2, 5, 3, 6, 4, 6, 4, 7, 5, 7, 5, 7, 5, 7, 5, 8, 5, 8, 5, 8, 6, 8, 6, 8, 7, 8, 8, 9, 8, 9, 8, 10, 8, 10, 9, 10, 9, 10, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,12

LINKS

Table of n, a(n) for n=1..81.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..floor((n-1)/2)} A280710(n-2i).

EXAMPLE

As 6 is a semiprime, we know that a(6 + 2*k) > 0 for k > 0.

MATHEMATICA

Table[Sum[MoebiusMu[n - 2 i]^2*KroneckerDelta[PrimeOmega[n - 2 i], 2], {i, Floor[(n - 1)/2]}], {n, 100}]

PROG

(PARI) a(n) = sum(i=1, (n-1)\2, bigomega(n-2*i)==2*issquarefree(n-2*i)); \\ Michel Marcus, Apr 11 2018

(PARI) upto(n) = {my(semiprimes = List(), res = vector(n)); forprime(p = 2, sqrtint(n), forprime(q = p+1, n \ p, listput(semiprimes, p * q))); for(i = 1, #semiprimes, forstep(j = semiprimes[i] + 2, n, 2, res[j]++)); res} \\ David A. Corneth, Apr 11 2018

CROSSREFS

Cf. A280710, A302604, A302642.

Sequence in context: A164960 A124137 A164092 * A319973 A025804 A042961

Adjacent sequences:  A302640 A302641 A302642 * A302644 A302645 A302646

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 10 2018

STATUS

approved

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Last modified September 17 06:03 EDT 2021. Contains 347478 sequences. (Running on oeis4.)