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).

2, 3, 4, 8, 9, 10, 16, 21, 27, 32, 50, 55, 64, 78, 81, 128, 136, 147, 171, 243, 250, 253, 256, 406, 465, 512, 605, 666, 729, 820, 903, 1014, 1024, 1029, 1081, 1250, 1378, 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

Offset: 1

Author

Antti Karttunen, Jan 16 2025

Keywords

• nonn

Examples

			55 = 5 * 11 is included, because floor(11/2) = 5.
666 = 2 * 3^2 * 37 is included, because floor(37/2) = 18 = 2 * 3^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A000244 (subsequences after their initial 1's), A379955 (characteristic function).

Cf. A000040, A130290.

Positions of terms > 1 in A217983.

Programs

Maple

N:= 10000: # for terms < N
R:= NULL:
p:= 1:
do
  p:= nextprime(p);
  a:= floor(p/2);
  if a*p > N then break fi;
  for e from 1 do
    x:= a*p^e;
    if x > N then break fi;
    R:= R,x;
  od
od:
sort([R]); # Robert Israel, Jan 16 2025

PARI

is_A379956 = A379955;