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A036668
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Hati numbers: of form 2^i*3^j*k, i+j even, (k,6)=1.
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19
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1, 4, 5, 6, 7, 9, 11, 13, 16, 17, 19, 20, 23, 24, 25, 28, 29, 30, 31, 35, 36, 37, 41, 42, 43, 44, 45, 47, 49, 52, 53, 54, 55, 59, 61, 63, 64, 65, 66, 67, 68, 71, 73, 76, 77, 78, 79, 80, 81, 83, 85, 89, 91, 92, 95, 96, 97, 99, 100, 101, 102, 103, 107
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OFFSET
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0,2
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COMMENTS
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Closed under multiplication. Each term is a product of a unique subset of {6} U A050376 \ {2,3}. - Peter Munn, Sep 14 2019
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LINKS
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FORMULA
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MAPLE
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N:= 1000: # to get all terms up to N
A:= {seq(2^i, i=0..ilog2(N))}:
Ae, Ao:= selectremove(issqr, A):
Be:= map(t -> seq(t*9^j, j=0 .. floor(log[9](N/t))), Ae):
Bo:= map(t -> seq(t*3*9^j, j=0..floor(log[9](N/(3*t)))), Ao):
B:= Be union Bo:
C1:= map(t -> seq(t*(6*i+1), i=0..floor((N/t -1)/6)), B):
C2:= map(t -> seq(t*(6*i+5), i=0..floor((N/t - 5)/6)), B):
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MATHEMATICA
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a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],
IntegerQ]]] &]], {150}]; a (* A036668 *)
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PROG
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(PARI) twos(n) = {local(r, m); r=0; m=n; while(m%2==0, m=m/2; r++); r}
threes(n) = {local(r, m); r=0; m=n; while(m%3==0, m=m/3; r++); r}
(PARI) list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 3), N=if(n%2, 2*3^n, 3^n); while(N<=lim, forstep(k=N, lim, [4*N, 2*N], listput(v, k)); N<<=2)); Set(v) \\ Charles R Greathouse IV, Sep 10 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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