A367481 Primitive practical numbers of the form 2 * 3^i * prime(k).

30, 42, 66, 78, 306, 342, 414, 522, 558, 666, 2214, 2322, 2538, 2862, 3186, 3294, 3618, 3834, 3942, 4266, 4482, 4806, 5238, 5454, 5562, 5778, 5886, 6102, 20574, 21222, 22194, 22518, 24138, 24462, 25434, 26406, 27054, 28026, 28998, 29322, 30942, 31266, 31914

Offset

1,1

Comments

This sequence and A308710 are both non-overlapping subsets of A267124.

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).

Terms are pseudoperfect numbers, A005835, but are not primitive pseudoperfect numbers, A006036.

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

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = 2 * 3^(floor(log_3(2*prime(n+2)))-1) * prime(n+2).

Mathematica

a[n_]:=2*3^(Floor[Log[2*Prime[n+2]]/Log[3]]-1)*Prime[n+2]; Array[a, 43] (* Stefano Spezia, Nov 19 2023 *)

Crossrefs

Cf. A000040, A000244, A005153, A005835, A006036, A233919, A267124, A308710.

Sequence in context: A342398 A226104 A091455 * A219742 A348557 A257832

Adjacent sequences: A367478 A367479 A367480 * A367482 A367483 A367484

Keyword

nonn

Author

Miko Labalan, Nov 19 2023

Status

approved