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

%I #11 Dec 31 2023 00:17:49

%S 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,

%T 38,41,43,44,46,47,49,50,52,53,58,59,61,62,64,67,68,71,73,74,76,79,81,

%U 82,83,86,89,92,94,97,98,101,103,106,107,109,113,116,118,121,122,124,125,127,128

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

%C 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.

%e 14 = 2*7 is a term since 4 < 7.

%e 44 = 4*11 is a term since 8 < 11.

%t 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]])]

%t a368087[m_, n_] := Select[Range[m, n], propQ]

%t a368087[1, 128]

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

%K nonn

%O 1,2

%A _Hartmut F. W. Hoft_, Dec 11 2023