

A082300


Numbers relatively prime to the sum of their prime factors (with repetition).


3



1, 6, 10, 12, 14, 15, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 40, 44, 45, 46, 48, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 68, 69, 74, 75, 76, 77, 80, 82, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 99, 104, 106, 108, 111, 112, 115, 116, 117, 118, 119, 122, 123, 124, 129, 133
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OFFSET

1,2


COMMENTS

In other words, numbers n such that n and sopfr(n) are relatively prime, where sopfr(n) (A001414) is the sum of the primes (with repetition) dividing n.
Conjecture: a(n) ~ (Pi^2/6)n.  Charles R Greathouse IV, Aug 04 2016
No term is prime since for prime p, p and 2p are not coprime; similarly no term is a prime power. A050703 is a subsequence because then n+sopfr(n) is prime, and so coprime to n.  David James Sycamore, Mar 04 2018


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

gcd(2*2*5,2+2+5) = gcd(2*2*5,3*3)=1, therefore 20 is a term;
gcd(3*11,3+11) = gcd(3*11,2*7)=1, therefore 33 is a term.


MATHEMATICA

Select[Range@ 106, CoprimeQ[#, Total@ Flatten@ Map[Table[#1, {#2}] & @@ # &, FactorInteger[#]]] &] (* Michael De Vlieger, Aug 06 2016 *)


PROG

(PARI) sopfr(n)=my(f=factor(n)); sum(i=1, #f~, f[i, 1]*f[i, 2])
is(n)=gcd(sopfr(n), n)==1 \\ Charles R Greathouse IV, Aug 04 2016


CROSSREFS

Cf. A001414, A275665, A050703.
A082299(a(n)) = 1.
Sequence in context: A097318 A080363 A289558 * A050703 A135711 A161543
Adjacent sequences: A082297 A082298 A082299 * A082301 A082302 A082303


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Apr 08 2003


EXTENSIONS

Revised definition from Lior Manor Apr 14 2004


STATUS

approved



