OFFSET
1,1
COMMENTS
Abundancy is defined as the ratio of the multiplicative sum-of-divisors function to the integer itself: abund(n) = sigma(n)/n. E.g., abund(10) = sigma(10) / 10 = (1+2+5+10) / 10 = 1.8 = 9 / 5.
Integers m and n are friendly if and only if they have the same abundancy. E.g., abund(12) = abund(234) = 7 / 3, so 12 and 234 are friends.
Integers which have no friends are called solitary.
The numbers in this sequence are solitary.
Compare abundancy to abundance as defined in A033880.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Claude W. Anderson and Dean Hickerson, Advanced Problem 6020: Friendly Integers, Amer. Math. Monthly, 1977, V84#1p65-6.
Walter Nissen, Primitive Friendly Integers and Exclusive Multiples, 2004 post to NMBRTHRY mailing list
MATHEMATICA
Select[Range[320], PrimeNu[#] > 1 && GCD[#, DivisorSigma[1, #]] == 1 &] (* Amiram Eldar, Jun 25 2019 *)
PROG
(PARI) isok(n) = (gcd(sigma(n), n) == 1) && (! isprime(n)) && (! (ispower(n, , &p) && isprime(p))); \\ Michel Marcus, Jan 24 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Nissen, Jul 08 2004
EXTENSIONS
Edited by Franklin T. Adams-Watters, Mar 06 2014
STATUS
approved