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A062760
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a(n) is n divided by the largest power of the squarefree kernel of n (A007947) which divides it.
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5
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 8, 1, 5, 1, 2, 1, 9, 1, 4, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 1, 8, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 2, 1, 1, 1, 16, 1, 7, 3, 1, 1, 1, 1, 4
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OFFSET
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1,12
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COMMENTS
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a(n) divides A003557 but is not equal to it.
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LINKS
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FORMULA
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EXAMPLE
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n=1800: the squarefree kernel is 2*3*5 = 30 and 900 = 30^2 divides n, a(1800) = 2, the quotient of 1800/900.
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MAPLE
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f:= proc(n) local F, m, t;
F:= ifactors(n)[2];
m:= min(seq(t[2], t=F));
mul(t[1]^(t[2]-m), t=F)
end proc:
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MATHEMATICA
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{1}~Join~Table[n/#^IntegerExponent[n, #] &@ Last@ Select[Divisors@ n, SquareFreeQ], {n, 2, 104}] (* Michael De Vlieger, Nov 02 2017 *)
a[n_] := Module[{f = FactorInteger[n], e}, e = Min[f[[;; , 2]]]; f[[;; , 2]] -= e; Times @@ Power @@@ f]; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)
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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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