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A173381
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a(n) = b_n(p_(n+1)) where p_n is the n-th prime, b_n(1)=1, b_n(2)=p_n, and for k>=3, b_n(k) is the smallest number larger than b_n(k-1) such that, for all i<k, b_n(k) is relatively prime to b_n(i) iff k is relatively prime to i.
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0
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3, 11, 31, 163, 661, 929, 2041, 21341, 15989, 47387, 125117, 263411, 123493, 10426601, 3654221, 4167127, 86622397, 4036267, 3910993, 541513877
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OFFSET
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1,1
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LINKS
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MAPLE
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b:= proc(n, k) option remember; local ok, m, i;
if k=1 then 1
elif k=2 then ithprime(n)
else for m from b(n, k-1)+1 do
ok:= true;
for i from 1 to k-1 do
if igcd(k, i)=1 xor igcd(m, b(n, i))=1
then ok:= false; break fi
od;
if ok then break fi
od; m
fi
end:
a:= n-> b(n, ithprime(n+1));
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MATHEMATICA
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b[n_, k_] := b[n, k] = Module[{ok, m, i}, Which[k==1, 1, k==2, Prime[n], True, For[m = b[n, k - 1] + 1, True, m++, ok = True; For[i = 1, i <= k - 1, i++, If[Xor[GCD[k, i]==1, GCD[m, b[n, i]]==1], ok = False; Break[]]]; If[ok, Break[]]]; m]];
a[n_] := b[n, Prime[n + 1]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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