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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 08 2003
EXTENSIONS
Revised definition from Lior Manor Apr 14 2004
STATUS
approved