OFFSET
1,1
COMMENTS
Sequence could be called the "odious-perfect numbers".
By the Euclid-Euler theorem, an even number k is perfect (A000396) if and only if k = 2^(m-1)*(2^m-1), where 2^m-1 is prime. From this it follows that all even perfect numbers greater than 6 have only odious divisors (A000069). Therefore, they all are in this sequence. However, the sequence also contains non-perfect numbers. The first two such numbers are 415800 and 2096128 (and no others up to 10^11). Comparing this sequence with A230587, one can see that the terms of this sequence are much rarer. It is an interesting phenomenon.
MATHEMATICA
okQ[n_] := DivisorSum[n, If[OddQ[Total[IntegerDigits[#, 2]]] && #<n, #, 0] &] == n; Reap[For[n=1, n<9*10^9, n++, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Dec 06 2015 *)
PROG
(PARI) is(n)=sumdiv(n, d, if(hammingweight(d)%2 && d<n, d))==n \\ Charles R Greathouse IV, Oct 24 2013
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
STATUS
approved