cp's OEIS Frontend

A273798 Numbers of the form 2^m*p where p is prime and p < 2^m.

%I A273798 #31 Jul 10 2020 11:41:18
%S A273798 8,12,16,24,32,40,48,56,64,80,96,112,128,160,176,192,208,224,256,320,
%T A273798 352,384,416,448,512,544,608,640,704,736,768,832,896,928,992,1024,
%U A273798 1088,1216,1280,1408,1472,1536,1664,1792,1856,1984,2048,2176,2368,2432,2560,2624,2752,2816,2944,3008,3072
%N A273798 Numbers of the form 2^m*p where p is prime and p < 2^m.
%C A273798 Number of terms <= 2^k: 0, 0, 1, 3, 5, 9, 13, 19, 25, 36, 47, 65, 83, 114, 145, 199, 253, 350, 447, …, .
%C A273798 Number of terms <= 2^k = Sum {i=2..k}, PrimePi( If( k < n/2, 2^k, 2^(n - k))).
%C A273798 Conjecture: a subsequence of A116882;
%C A273798 Terms in A116882 but not here: 1, 2, 4, 144, 240, 288, 480, 576, 672, 800, 864, 960, 1152, ... ; or more simply 1, 2, 4 and powers of 2 times 144, 240, 672, 800, 864, 2112, 2240, 2496, 2880, 3136, ...
%H A273798 Robert G. Wilson v, <a href="/A273798/b273798.txt">Table of n, a(n) for n = 1..1000</a>
%t A273798 f[n_] := Block[{p = Prime@ Range@ PrimePi[2^n - 1]}, 2^n* p]; Take[ Sort@ Flatten@ Array[f, 10], 57]
%o A273798 (PARI) isok(n) = my(m = valuation(n, 2)); (isprime(p=n/2^m) && (p < 2^m)) || ((m > 2) && (n==2^m)); \\ _Michel Marcus_, Aug 31 2016
%Y A273798 Cf. A116882.
%K A273798 nonn
%O A273798 1,1
%A A273798 _Robert G. Wilson v_, May 30 2016