A368087 Numbers of the form 2^k * p^s with k>=0, s>=0, p>2 prime and 2^(k+1) < p.

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 26, 27, 29, 31, 32, 34, 37, 38, 41, 43, 44, 46, 47, 49, 50, 52, 53, 58, 59, 61, 62, 64, 67, 68, 71, 73, 74, 76, 79, 81, 82, 83, 86, 89, 92, 94, 97, 98, 101, 103, 106, 107, 109, 113, 116, 118, 121, 122, 124, 125, 127, 128

Offset

1,2

Comments

This sequence is a subsequence of A174905 = A241008 union A241010. The symmetric representation of sigma (cf. A237593) for a number m in this sequence consists of s+1 parts, the number of odd divisors of m, each part having width 1.

Links

Table of n, a(n) for n=1..70.

Example

14 = 2*7 is a term since 4 < 7.
44 = 4*11 is a term since 8 < 11.

Mathematica

propQ[n_] := Module[{fL=FactorInteger[n]}, Length[fL]==1||(Length[fL]==2&&fL[[1, 1]]==2&&fL[[1, 1]]^(fL[[1, 2]]+1)<fL[[2, 1]])]
a368087[m_, n_] := Select[Range[m, n], propQ]
a368087[1, 128]

Crossrefs

Cf. A005279, A174905, A235791, A237048, A237270, A237593, A241008, A241010, A249223, A341969.

Sequence in context: A129511 A174905 A260402 * A191849 A055019 A261466

Adjacent sequences: A368084 A368085 A368086 * A368088 A368089 A368090

Keyword

nonn

Author

Hartmut F. W. Hoft, Dec 11 2023

Status

approved