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A192498
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Smallest prime p such that there is a gap of tau(n) between p and the next prime, otherwise 0.
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1
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2, 3, 3, 0, 3, 7, 3, 7, 0, 7, 3, 23, 3, 7, 7, 0, 3, 23, 3, 23, 7, 7, 3, 89, 0, 7, 7, 23, 3, 89, 3, 23, 7, 7, 7, 0, 3, 7, 7, 89, 3, 89, 3, 23, 23, 7, 3, 139, 0, 23, 7, 23, 3, 89, 7, 89, 7, 7, 3, 199, 3, 7, 23, 0, 7, 89, 3, 23, 7, 89, 3, 199, 3, 7, 23, 23, 7
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OFFSET
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1,1
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COMMENTS
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For n > 1, a(n)=0 if n is a perfect square (see A048691) because then tau(n) is odd.
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LINKS
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FORMULA
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EXAMPLE
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a(12) = 23 because 29 - 23 = 6 = tau(12).
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MAPLE
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A000230 := proc(g) if g = 1 then return 2 ; elif type(g, 'odd') then return 0 ; else for i from 1 do if ithprime(i+1)-ithprime(i) = g then return ithprime(i) ; end if; end do: end if; end proc:
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MATHEMATICA
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Module[{nn=200, prs, dfs, thr}, prs=Prime[Range[nn]]; dfs=Differences[prs]; thr = DeleteDuplicatesBy[Thread[{Most[prs], dfs}], Last]; Join[{2}, Flatten[ Table[ Select[thr, #[[2]]==DivisorSigma[0, n]&], {n, 2, 80}]/.{}->{{0, 0}}, 1][[All, 1]]]] (* Harvey P. Dale, Mar 09 2021 *)
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PROG
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(PARI)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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