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

2,1

Comments

a(n) = A032742(n) + A020639(n) - 1; a(n) <= n and for n > 1 a(n) = n iff n is prime.

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A318678 A119674 A064920 * A062854 A057859 A242992

Adjacent sequences: A064913 A064914 A064915 * A064917 A064918 A064919

Keyword

nonn

Author

Reinhard Zumkeller, Oct 14 2001

Status

approved