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%I #23 Dec 01 2023 16:03:44
%S 30,42,66,78,306,342,414,522,558,666,2214,2322,2538,2862,3186,3294,
%T 3618,3834,3942,4266,4482,4806,5238,5454,5562,5778,5886,6102,20574,
%U 21222,22194,22518,24138,24462,25434,26406,27054,28026,28998,29322,30942,31266,31914
%N Primitive practical numbers of the form 2 * 3^i * prime(k).
%C This sequence and A308710 are both non-overlapping subsets of A267124.
%C a(n) is a number of the form 2 * 3^i * prime(k) for i > 0 and b(i) < k <= b(i+1) where b(n) = Sum_{m=2..n+1} A233919(m).
%C Terms are pseudoperfect numbers, A005835, but are not primitive pseudoperfect numbers, A006036.
%C Since no term is a square or twice a square, there are no terms k such that sigma(k) is odd. Therefore, according to Proposition 10 by Rao/Peng (see their JNT paper at A083207) all terms are Zumkeller numbers. - _Ivan N. Ianakiev_, Nov 28 2023
%F a(n) = 2 * 3^(floor(log_3(2*prime(n+2)))-1) * prime(n+2).
%t a[n_]:=2*3^(Floor[Log[2*Prime[n+2]]/Log[3]]-1)*Prime[n+2]; Array[a,43] (* _Stefano Spezia_, Nov 19 2023 *)
%Y Cf. A000040, A000244, A005153, A005835, A006036, A233919, A267124, A308710.
%K nonn
%O 1,1
%A _Miko Labalan_, Nov 19 2023
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