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A130064
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a(n) = (n / SmallestPrimeFactor(n)) * GreatestPrimeFactor(n).
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7
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1, 2, 3, 4, 5, 9, 7, 8, 9, 25, 11, 18, 13, 49, 25, 16, 17, 27, 19, 50, 49, 121, 23, 36, 25, 169, 27, 98, 29, 75, 31, 32, 121, 289, 49, 54, 37, 361, 169, 100, 41, 147, 43, 242, 75, 529, 47, 72, 49, 125, 289, 338, 53, 81, 121, 196, 361, 841, 59, 150, 61, 961, 147, 64, 169, 363
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) >= n.
Sum_{k=1..n} k/a(k) ~ n/log(n) + 3*n/log(n)^2 + o(n/log(n)^2) (Erdős and van Lint, 1982). - Amiram Eldar, Oct 14 2022
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MATHEMATICA
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a[n_] := With[{pp = FactorInteger[n][[All, 1]]}, n*pp[[-1]]/pp[[1]]];
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PROG
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(PARI) a(n) = if (n==1, 1, my(f=factor(n)[, 1]~); n*vecmax(f)/vecmin(f)); \\ Michel Marcus, Sep 24 2022
(Python)
from sympy import factorint
def a(n): f = factorint(n); return 1 if n == 1 else n//min(f)*max(f)
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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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