A064916 a(n) = n/lpf(n) + lpf(n) - 1, where lpf = A020639 = least prime factor.

2, 3, 3, 5, 4, 7, 5, 5, 6, 11, 7, 13, 8, 7, 9, 17, 10, 19, 11, 9, 12, 23, 13, 9, 14, 11, 15, 29, 16, 31, 17, 13, 18, 11, 19, 37, 20, 15, 21, 41, 22, 43, 23, 17, 24, 47, 25, 13, 26, 19, 27, 53, 28, 15, 29, 21, 30, 59, 31, 61, 32, 23, 33, 17, 34, 67, 35, 25, 36, 71, 37, 73, 38, 27

Offset: 2

Author

Reinhard Zumkeller, Oct 14 2001

Keywords

• nonn

Comments

a(n) = A032742(n) + A020639(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

• Harvey P. Dale, Table of n, a(n) for n = 2..1001

Crossrefs

Cf. A064920, A064917, A064918, A032742, A020639, A064919.

Programs

Mathematica

lpf[n_]:=Module[{lp=FactorInteger[n][[1,1]]},n/lp+lp-1]; Array[lpf, 80, 2] (* Harvey P. Dale, Sep 25 2011 *)

PARI

lpf(n)= { local(f); f=factor(n); return(f[1, 1]) } { for (n=2, 1000, L=lpf(n); a=n / L + L - 1; write("b064916.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 28 2009

PARI

a(n) = my(p = vecmin(factor(n)[,1])); n/p + p - 1; \\ Michel Marcus, Jun 19 2018