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

2,1

Comments

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

Links

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

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

Crossrefs

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

Sequence in context: A296075 A318678 A119674 * A064916 A062854 A057859

Adjacent sequences: A064917 A064918 A064919 * A064921 A064922 A064923

Keyword

nice,nonn

Author

Reinhard Zumkeller, Oct 14 2001

Status

approved