OFFSET
1,1
COMMENTS
All numbers in the sequence are pseudoperfect numbers since n = Sum_{i=0..m-1} (2^i * q) + Sum_{i=0..m} (2^i * q/p).
The first pseudoperfect number not in this sequence is A005835(2) = 12 = 2^2 * 3 since 3 is the first, not the second Mersenne prime.
The first pseudoperfect number in this sequence that is not in A352030 is 90 = 2*3*3*5 since its symmetric representation of sigma consists of one part with maximum width 3.
Since p = 2^(m+1) - 1 < 2^(m+1) the maximum width of the symmetric representation of sigma(a(n)) is at least 2, for all n.
EXAMPLE
MATHEMATICA
evenoddPartsQ[n_] := Module[{dL=Select[Divisors[n], OddQ], fL=First[FactorInteger[n]], evenE}, evenE=If[First[fL]==2, Last[fL], 0]; n/2^evenE>1&&dL[[2]]==2^(evenE+1)-1]
a352061[n_] := Select[Range[n], evenoddPartsQ]
a352061[600]
CROSSREFS
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Mar 04 2022
STATUS
approved