%I #37 Sep 08 2022 08:46:09

%S 1,4,8,32,128,256,512,1024,4096,8192,16384,32768,65536,131072,262144,

%T 524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,

%U 134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592,17179869184,34359738368

%N Numbers of the form 2^k (k>=0) that are a sum of divisors of n for some n.

%C Set of values A094502(n) = sigma(A046528(n)) in increasing order.

%C Complement of A094505 with respect to A000079 (powers of 2).

%C Corresponding values of numbers k>0 are in A180221.

%F a(1) = 1, for n>=2, a(n) = 2^A180221(n-1).

%e 32 = 2^5 is in sequence because there are numbers n = 21 and 31 with sigma(n) = 32.

%o (Magma) Set(Sort([SumOfDivisors(n): n in [A046528(n)]]))

%o (Magma) Set(Sort([SumOfDivisors(n): n in[1..10000], k in [0..100] | SumOfDivisors(n) eq 2^k]))

%o (Magma) [1] cat [2^n: n in[A180221(n)]]

%Y Cf. A000079, A000203, A046528, A078426, A094502, A094505, A180221.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Feb 27 2015