A275665 Numbers n such that n and sopf(n) are relatively prime, where sopf(n) (A008472) is the sum of the distinct primes dividing n.

1, 6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 85, 86, 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

Offset: 1

Author

Charles R Greathouse IV, Aug 04 2016

Keywords

• nonn

Comments

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

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• R. B. Hall, On the probability that n and f(n) are relatively prime, Acta Arithmetica 17 (1970), pp. 169-183.

Crossrefs

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

Programs

Mathematica

Select[Range@ 165, CoprimeQ[#, Total@ FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Aug 06 2016 *)

PARI

sopf(n)=vecsum(factor(n)[,1])
is(n)=gcd(sopf(n),n)==1