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

1,2

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A007774 A030231 A267114 * A056760 A328956 A084227

Adjacent sequences: A275662 A275663 A275664 * A275666 A275667 A275668

Keyword

nonn

Author

Charles R Greathouse IV, Aug 04 2016

Status

approved