

A237417


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


2



3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 21, 23, 24, 27, 29, 30, 33, 34, 35, 36, 39, 40, 42, 43, 45, 46, 48, 51, 53, 54, 55, 57, 58, 60, 63, 65, 66, 68, 70, 71, 72, 78, 80, 83, 84, 85, 86, 89, 90, 92, 93, 95, 96, 99, 101, 102, 105, 106, 108, 110, 111, 113, 114, 116, 117, 119, 120, 123, 126, 129
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OFFSET

1,1


COMMENTS

Odiousfree*evilfree numbers: numbers of the form odiousfree*evilfree.
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,...
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.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A093688(k+1)*A093696(m).


MAPLE

N:= 200: # to get all terms <= N
Ofree:= {$2..N}: Efree:= {$1..N/3}:
for n from 2 to N do
t:= convert(convert(n, base, 2), `+`) mod 2;
if t = 0 then Efree:= Efree minus {seq(i, i=n..N/3, n)}
else Ofree:= Ofree minus {seq(i, i=n..N, n)}
fi
od:
sort(convert(select(`<=`, {seq(seq(s*t, s=Ofree), t=Efree)}, N), list)); # Robert Israel, May 09 2019


MATHEMATICA

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 *)


PROG

(PARI) isA093696(n)= fordiv(n, d, if(hammingweight(d)%2==0, return(0))); 1;
isA093688(n)= if (n==1, 0, sumdiv(n, d, hammingweight(d)%2)==1);
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


CROSSREFS

Cf. A093688, A093696.
Sequence in context: A325428 A239064 A227455 * A165740 A241571 A080307
Adjacent sequences: A237414 A237415 A237416 * A237418 A237419 A237420


KEYWORD

nonn,base


AUTHOR

Irina Gerasimova, Feb 23 2014, following a suggestion from JuriStepan Gerasimov


EXTENSIONS

Definition corrected by Jon E. Schoenfield, Feb 26 2014


STATUS

approved



