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A100573
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Smallest difference between distinct prime divisors of n, or 0 if n is a prime power.
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2
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0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 5, 2, 0, 0, 1, 0, 3, 4, 9, 0, 1, 0, 11, 0, 5, 0, 1, 0, 0, 8, 15, 2, 1, 0, 17, 10, 3, 0, 1, 0, 9, 2, 21, 0, 1, 0, 3, 14, 11, 0, 1, 6, 5, 16, 27, 0, 1, 0, 29, 4, 0, 8, 1, 0, 15, 20, 2, 0, 1, 0, 35, 2, 17, 4, 1, 0, 3, 0, 39, 0, 1, 12, 41, 26, 9, 0, 1, 6, 21, 28, 45
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OFFSET
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1,10
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LINKS
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EXAMPLE
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For 30 = 2*3*5, 2 and 3 are separated by only 1, so a(30) = 1.
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MATHEMATICA
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<<NumberTheory`NumberTheoryFunctions` pfl[x_] :=PrimeFactorList[x] pd[x_] :=Delete[RotateLeft[pfl[x]]-pfl[x], -1] Table[Min[pd[w]], {w, 1, 1000}] (* Labos *)
Table[Min[Differences[Transpose[FactorInteger[n]][[1]]]], {n, 100}]/.\[Infinity]->0 (* Harvey P. Dale, Jul 27 2015 *)
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PROG
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(PARI) A100573(n) = if(omega(n)<=1, 0, my(ps=factor(n)[, 1]); vecmin(vector((#ps)-1, i, ps[i+1]-ps[i]))); \\ Antti Karttunen, Mar 03 2018
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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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