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A095134 Sum of the product of the first ceiling(n/2) odd-indexed primes and the product of the first floor(n/2) even-indexed primes; a(1) = 2.

%I A095134 #18 Dec 03 2024 12:25:33
%S A095134 2,5,13,31,131,383,2143,7057,48197,193433,1483733,6898961,60231361,
%T A095134 293988703,2808611363,15253406999,164272132459,925319250199,
%U A095134 10930128162979,65091314708809,796351893424729,5081275480436251
%N A095134 Sum of the product of the first ceiling(n/2) odd-indexed primes and the product of the first floor(n/2) even-indexed primes; a(1) = 2.
%H A095134 Robert Israel, <a href="/A095134/b095134.txt">Table of n, a(n) for n = 1..631</a>
%F A095134 Sum_{i=1..n} of the product_{j=2..n, 2} p_j (A066206) and the product_{k=1..n, 2} p_j (A066205).
%e A095134 a(5) = 2*5*11 + 3*7 = 131, a(6) = 2*5*11 + 3*7*13 = 383;
%e A095134 a(7) = 2*5*11*17 + 3*7*13 = 2143, a(8) = 2*5*11*17 + 3*7*13*19 = 7057.
%p A095134 p:= 2: R:= 2: a:= 2: b:= 1:
%p A095134 for m from 1 to 10 do
%p A095134   p:= nextprime(p); b:= b*p; R:= R,a+b;
%p A095134   p:= nextprime(p); a:= a*p; R:= R,a+b;
%p A095134 od:
%p A095134 R; # _Robert Israel_, Dec 01 2024
%t A095134 f[n_] := Product[Prime[i], {i, 2, n, 2}] + Product[Prime[i], {i, 1, n, 2}]; f[1] = 2; Table[ f[n], {n, 22}]
%o A095134 (PARI) a(n) = if (n==1, 2, vecprod(vector(floor(n/2), k, prime(2*k)))+vecprod(vector(ceil(n/2), k, prime(2*k-1)))); \\ _Michel Marcus_, Dec 03 2024
%Y A095134 Cf. A095137, A000040, A066206, A066205.
%K A095134 nonn
%O A095134 1,1
%A A095134 _Robert G. Wilson v_, May 27 2004