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Revision History for A303119

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Number of partitions of n into two parts (p,q) with p <= q such that p is semiprime and q is squarefree.
(history; published version)

#6 by Wesley Ivan Hurt at Thu Jun 20 04:39:31 EDT 2019

STATUS

editing

approved

#5 by Wesley Ivan Hurt at Thu Jun 20 04:38:38 EDT 2019

FORMULA

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

STATUS

approved

editing

#4 by Susanna Cuyler at Thu Apr 19 08:39:39 EDT 2018

STATUS

proposed

approved

#3 by Wesley Ivan Hurt at Wed Apr 18 20:57:20 EDT 2018

STATUS

editing

proposed

#2 by Wesley Ivan Hurt at Wed Apr 18 20:56:00 EDT 2018

NAME

allocated for Wesley Ivan HurtNumber of partitions of n into two parts (p,q) with p <= q such that p is semiprime and q is squarefree.

DATA

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 3, 3, 1, 4, 2, 3, 2, 3, 3, 3, 3, 3, 4, 3, 2, 4, 4, 4, 3, 4, 4, 4, 3, 6, 7, 6, 3, 6, 6, 4, 4, 7, 8, 5, 3, 7, 8, 7, 3, 6, 6, 7, 5, 7, 6, 6, 5, 8, 10, 6, 5, 8, 10, 8, 6, 8, 11, 9, 6, 9, 12, 10, 7, 9, 9, 7

OFFSET

1,17

LINKS

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

FORMULA

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

MATHEMATICA

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

CROSSREFS

Cf. A001222, A008683, A302538.

KEYWORD

allocated

nonn,easy

AUTHOR

Wesley Ivan Hurt, Apr 18 2018

STATUS

approved

editing

#1 by Wesley Ivan Hurt at Wed Apr 18 20:56:00 EDT 2018

NAME

allocated for Wesley Ivan Hurt

KEYWORD

allocated

STATUS

approved