A082300 Numbers relatively prime to the sum of their prime factors (with repetition).

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

Offset: 1

Author

Reinhard Zumkeller, Apr 08 2003

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001414, A275665, A050703.

A082299(a(n)) = 1.

Programs

Mathematica

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

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

Extensions

Revised definition from Lior Manor, Apr 14 2004