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A064920
a(n) = n/gpf(n) + gpf(n) - 1, where gpf = A006530 = greatest prime factor.
6
2, 3, 3, 5, 4, 7, 5, 5, 6, 11, 6, 13, 8, 7, 9, 17, 8, 19, 8, 9, 12, 23, 10, 9, 14, 11, 10, 29, 10, 31, 17, 13, 18, 11, 14, 37, 20, 15, 12, 41, 12, 43, 14, 13, 24, 47, 18, 13, 14, 19, 16, 53, 20, 15, 14, 21, 30, 59, 16, 61, 32, 15, 33, 17, 16, 67, 20, 25, 16, 71, 26, 73, 38, 19, 22
OFFSET
2,1
COMMENTS
a(n) = A052126(n) + A006530(n) - 1; a(n) <= n and for n > 1: a(n) = n iff n is prime.
LINKS
EXAMPLE
a(18) = 18/2 + 2 - 1 = 10;
a(19) = 19/19 + 19 - 1 = 19.
MATHEMATICA
a[n_] := (g = FactorInteger[n][[-1, 1]]; n/g + g - 1); a /@ Range[2, 76] (* Jean-François Alcover, Apr 06 2011 *)
PROG
(PARI) gpf(n)= { local(f); f=factor(n)~; return(f[1, length(f)]) } { for (n=2, 1000, g=gpf(n); a=n / g + g - 1; write("b064920.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 29 2009
(PARI) a(n) = my(p = vecmax(factor(n)[, 1])); n/p + p - 1; \\ Michel Marcus, Jun 19 2018
KEYWORD
nice,nonn
AUTHOR
Reinhard Zumkeller, Oct 14 2001
STATUS
approved