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

8, 12, 16, 24, 32, 40, 48, 56, 64, 80, 96, 112, 128, 160, 176, 192, 208, 224, 256, 320, 352, 384, 416, 448, 512, 544, 608, 640, 704, 736, 768, 832, 896, 928, 992, 1024, 1088, 1216, 1280, 1408, 1472, 1536, 1664, 1792, 1856, 1984, 2048, 2176, 2368, 2432, 2560, 2624, 2752, 2816, 2944, 3008, 3072

Offset: 1

Author

Robert G. Wilson v, May 30 2016

Keywords

• nonn

Comments

Number of terms <= 2^k: 0, 0, 1, 3, 5, 9, 13, 19, 25, 36, 47, 65, 83, 114, 145, 199, 253, 350, 447, …, .

Number of terms <= 2^k = Sum {i=2..k}, PrimePi( If( k < n/2, 2^k, 2^(n - k))).

Conjecture: a subsequence of A116882;

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, ...

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A116882.

Programs

Mathematica

f[n_] := Block[{p = Prime@ Range@ PrimePi[2^n - 1]}, 2^n* p]; Take[ Sort@ Flatten@ Array[f, 10], 57]

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