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A141100 Number of unordered pairs of odd composite numbers that sum to 2n. 7

%I

%S 0,0,0,0,0,0,0,0,1,0,0,1,0,0,2,0,1,2,0,1,3,1,1,3,2,1,4,1,2,5,1,3,5,1,

%T 4,5,3,3,6,3,3,7,3,3,9,3,4,7,4,6,9,5,5,8,6,6,10,5,5,12,4,6,12,5,9,11,

%U 7,7,11,9,9,13,8,8,16,7,11,14,8,11,14,9,9,17,13,10,16,11,11,19,11,12,18,10

%N Number of unordered pairs of odd composite numbers that sum to 2n.

%C See A141099 for pairs of odd nonprime numbers. We have a(n) > 0 except for the 14 values of 2n given in A118081.

%H T. D. Noe, <a href="/A141100/b141100.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) = 1 - floor(n/2) + sum_{i=3..n} A005171(i) * A005171(2n-i), n>1. - _Wesley Ivan Hurt_, Dec 27 2013

%e a(18)=2 because 36 = 9+27 = 15+21.

%t Table[cnt=0; Do[If[ !PrimeQ[i] && !PrimeQ[2n-i], cnt++ ], {i,3,n,2}]; cnt, {n,100}]

%Y Cf. A141095, A141097.

%K nonn

%O 1,15

%A _T. D. Noe_, Jun 02 2008, Jun 05 2008

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Last modified February 3 21:17 EST 2023. Contains 360045 sequences. (Running on oeis4.)