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A060654
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a(n) = gcd(n, A060766(n)).
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1
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1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 7, 11, 1, 12, 5, 13, 9, 14, 1, 30, 1, 16, 11, 17, 7, 18, 1, 19, 13, 20, 1, 21, 1, 22, 15, 23, 1, 24, 7, 25, 17, 26, 1, 27, 11, 28, 19, 29, 1, 60, 1, 31, 21, 32, 13, 33, 1, 34, 23, 70, 1, 36, 1, 37, 25, 38, 11, 39, 1, 40, 27, 41
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OFFSET
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2,3
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LINKS
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FORMULA
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a(n) = gcd(n, lcm(dd(n))), where dd(n) is the first difference of divisors (ordered by size).
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EXAMPLE
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If n is prime p, then A060766(p) = p-1 and lcm(p, p-1) = 1. If n=2k then a(2k)=k or as an "anomaly", a(2k)=2k.
At n=30, D={1, 2, 3, 5, 6, 10, 15, 30}, dD={1, 1, 2, 1, 4, 5, 15}={1, 2, 4, 5, 15}, lcm(dD)=60, gcd(n, lcm(dD(n))) = gcd(30, 60) = 30 = n.
At n=36, D={1, 2, 3, 4, 6, 9, 12, 18, 36}, dD={1, 1, 1, 2, 3, 3, 6, 18}={1, 2, 3, 6, 18}, lcm(dD)=18, gcd(n, lcm(dD(n))) = gcd(36, 18) = 18 = n/2.
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MAPLE
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A060766:= proc(n) local F; F:= sort(convert(numtheory:-divisors(n), list));
ilcm(op(F[2..-1] - F[1..-2])) end proc:
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MATHEMATICA
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Table[GCD[n, LCM @@ Differences@ Divisors@ n], {n, 2, 82}] (* Michael De Vlieger, Dec 20 2015 *)
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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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