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A237417 Numbers that are the product of an odiousfree number and an evilfree number.

%I A237417 #41 Oct 17 2020 02:18:44
%S A237417 3,5,6,9,10,12,15,17,18,20,21,23,24,27,29,30,33,34,35,36,39,40,42,43,
%T A237417 45,46,48,51,53,54,55,57,58,60,63,65,66,68,70,71,72,78,80,83,84,85,86,
%U A237417 89,90,92,93,95,96,99,101,102,105,106,108,110,111,113,114,116,117,119,120,123,126,129
%N A237417 Numbers that are the product of an odiousfree number and an evilfree number.
%C A237417 Odiousfree*evilfree numbers: numbers of the form odiousfree*evilfree.
%C A237417 Subsequence of this sequence (A237417): numbers that are not the products of two odious numbers or the products of two evil numbers: 3, 5, 6, 10, 12, 17, 20, 23, 24, 29, 33, 34, 39, 40, 43, 46, 48, 57, 58, 63, 65, 66, 68, 71, 78, 80, 83, 86, 89, 92, 95, 101, 105, 106, 111, 113, 114, 116, 119,...
%C A237417 Putting the 1 aside in A093688, these could be called odiousfree numbers, and are a subsequence of A001969. A093696 would be the evilfree numbers then, and are a subsequence of A000069.
%H A237417 Robert Israel, <a href="/A237417/b237417.txt">Table of n, a(n) for n = 1..10000</a>
%F A237417 a(n) = A093688(k+1)*A093696(m).
%p A237417 N:= 200: # to get all terms <= N
%p A237417 Ofree:= {$2..N}: Efree:= {$1..N/3}:
%p A237417 for n from 2 to N do
%p A237417   t:= convert(convert(n,base,2),`+`) mod 2;
%p A237417   if t = 0 then Efree:= Efree minus {seq(i,i=n..N/3,n)}
%p A237417   else Ofree:= Ofree minus {seq(i,i=n..N,n)}
%p A237417   fi
%p A237417 od:
%p A237417 sort(convert(select(`<=`,{seq(seq(s*t,s=Ofree),t=Efree)},N),list)); # _Robert Israel_, May 09 2019
%t A237417 odFreeQ[n_] := AllTrue[Rest @ Divisors[n], EvenQ[DigitCount[#, 2, 1]] &]; evFreeQ[n_] := AllTrue[Divisors[n], OddQ[DigitCount[#, 2, 1]] &]; m = 100; o = Select[Range[2, m], odFreeQ]; e = Select[Range[m], evFreeQ]; Union @ Select[Times @@@ Tuples[{o, e}], # <= m &] (* _Amiram Eldar_, Oct 16 2020 *)
%o A237417 (PARI) isA093696(n)= fordiv(n, d, if(hammingweight(d)%2==0, return(0))); 1;
%o A237417 isA093688(n)= if (n==1, 0, sumdiv(n, d, hammingweight(d)%2)==1);
%o A237417 lista(nn) = {vn = vector(2*nn, i, i); vof = select(n->isA093696(n), vn); vef = select(n->isA093688(n), vn); vp = []; for (i = 1, #vof, for (j = 1, #vef, vp = Set(concat(vp, vof[i]*vef[j])););); for (i = 1, #vp, if (vp[i] <= nn, print1(vp[i], ", ")););} \\ _Michel Marcus_, Mar 05 2014
%Y A237417 Cf. A093688, A093696.
%K A237417 nonn,base
%O A237417 1,1
%A A237417 _Irina Gerasimova_, Feb 23 2014, following a suggestion from _Juri-Stepan Gerasimov_
%E A237417 Definition corrected by _Jon E. Schoenfield_, Feb 26 2014