

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.


2



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
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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. 169183.


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



