OFFSET
1,1
COMMENTS
Prime p is in the sequence, if and only if p, p^2, p^3, p^4, p^2+1 and p^2+p all are odious (A000069). We conjecture that the sequence contains also composite numbers, but the first one should be very large.
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..2500
FORMULA
A230500((a(n)+1)/2)>=4.
EXAMPLE
59^2=3481 is odious together with 59, 59^3=205379, 59^4=12117361, 59^2+1=3482 and 59^2 + 59=3540. Thus 59 is in the sequence.
MATHEMATICA
odiousQ[n_]:=OddQ[DigitCount[n, 2][[1]]]; selQ[n_]:=Apply[And, Map[odiousQ, Flatten[Map[{n+#, n*#, n/ #}&, Divisors[n]]]]]; Sqrt[Select[Range[3, 5000]^2, (!PrimeQ[#]) && OddQ[#] && odiousQ[#] && selQ[#]&]] (* Peter J. C. Moses, Nov 16 2013 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Nov 16 2013
STATUS
approved