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

1,2

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 A361126 A330397

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