A064920 a(n) = n/gpf(n) + gpf(n) - 1, where gpf = A006530 = greatest prime factor.

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

Author

Reinhard Zumkeller, Oct 14 2001

Keywords

• nice
• nonn

Comments

a(n) = A052126(n) + A006530(n) - 1; a(n) <= n and for n > 1: a(n) = n iff n is prime.

Examples

			a(18) = 18/2 + 2 - 1 = 10;
a(19) = 19/19 + 19 - 1 = 19.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A064916, A064921, A064922, A006530, A052126, A064923, A064924.

Programs

Mathematica

a[n_] := (g = FactorInteger[n][[-1, 1]]; n/g + g - 1); a /@ Range[2, 76] (* Jean-François Alcover, Apr 06 2011 *)

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