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A379956 Numbers k that can be expressed in the form k = floor(prime(i)/2) * prime(i)^e, for some e, i > 0, where prime(i) = A000040(i).

%I A379956 #10 Jan 17 2025 02:41:28
%S A379956 2,3,4,8,9,10,16,21,27,32,50,55,64,78,81,128,136,147,171,243,250,253,
%T A379956 256,406,465,512,605,666,729,820,903,1014,1024,1029,1081,1250,1378,
%U A379956 1711,1830,2048,2187,2211,2312,2485,2628,3081,3249,3403,3916,4096,4656,5050,5253,5671,5819,5886,6250,6328,6561,6655,7203,8001
%N A379956 Numbers k that can be expressed in the form k = floor(prime(i)/2) * prime(i)^e, for some e, i > 0, where prime(i) = A000040(i).
%H A379956 Robert Israel, <a href="/A379956/b379956.txt">Table of n, a(n) for n = 1..10000</a>
%e A379956 55 = 5 * 11 is included, because floor(11/2) = 5.
%e A379956 666 = 2 * 3^2 * 37 is included, because floor(37/2) = 18 = 2 * 3^2.
%p A379956 N:= 10000: # for terms < N
%p A379956 R:= NULL:
%p A379956 p:= 1:
%p A379956 do
%p A379956   p:= nextprime(p);
%p A379956   a:= floor(p/2);
%p A379956   if a*p > N then break fi;
%p A379956   for e from 1 do
%p A379956     x:= a*p^e;
%p A379956     if x > N then break fi;
%p A379956     R:= R,x;
%p A379956   od
%p A379956 od:
%p A379956 sort([R]); # _Robert Israel_, Jan 16 2025
%o A379956 (PARI) is_A379956 = A379955;
%Y A379956 Cf. A000079, A000244 (subsequences after their initial 1's), A379955 (characteristic function).
%Y A379956 Cf. A000040, A130290.
%Y A379956 Positions of terms > 1 in A217983.
%K A379956 nonn
%O A379956 1,1
%A A379956 _Antti Karttunen_, Jan 16 2025