A275665 - OEIS

%I #16 Aug 23 2016 12:38:04

%S 1,6,10,12,14,15,18,20,21,22,24,26,28,33,34,35,36,38,39,40,44,45,46,

%T 48,50,51,52,54,55,56,57,58,62,63,65,68,69,72,74,75,76,77,80,82,85,86,

%U 87,88,91,92,93,94,95,96,98,99,100,104,106,108,111,112,115,116,117,118,119,122,123,124,129,133,134,135,136,141,142,143,144,145,146,147,148,152,153,155,158,159,160,161,162,164,165

%N Numbers n such that n and sopf(n) are relatively prime, where sopf(n) (A008472) is the sum of the distinct primes dividing n.

%C Hall shows that the density of this sequence is 6/Pi^2, so a(n) ~ (Pi^2/6)n.

%C Differs from A267114, from A030231, and from A007774 (shifted by one index) first at n=93. - _R. J. Mathar_, Aug 22 2016

%H Charles R Greathouse IV, <a href="/A275665/b275665.txt">Table of n, a(n) for n = 1..10000</a>

%H R. B. Hall, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa17/aa1724.pdf">On the probability that n and f(n) are relatively prime</a>, Acta Arithmetica 17 (1970), pp. 169-183.

%t Select[Range@ 165, CoprimeQ[#, Total@ FactorInteger[#][[All, 1]]] &] (* _Michael De Vlieger_, Aug 06 2016 *)

%o (PARI) sopf(n)=vecsum(factor(n)[,1])

%o is(n)=gcd(sopf(n),n)==1

%Y Cf. A008472, A082300, A267114, A030231, A007774.

%K nonn

%O 1,2

%A _Charles R Greathouse IV_, Aug 04 2016