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A095738 Numbers that are coprime to sigma but are not prime powers.

%I A095738 #27 Jun 25 2019 18:35:20
%S A095738 21,35,36,39,50,55,57,63,65,75,77,85,93,98,100,111,115,119,129,133,
%T A095738 143,144,155,161,171,175,183,185,187,189,201,203,205,209,215,217,219,
%U A095738 221,225,235,237,242,245,247,253,259,265,275,279,291,299,301,305,309,319
%N A095738 Numbers that are coprime to sigma but are not prime powers.
%C A095738 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.
%C A095738 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.
%C A095738 Integers which have no friends are called solitary.
%C A095738 The numbers in this sequence are solitary.
%C A095738 Compare abundancy to abundance as defined in A033880.
%H A095738 Amiram Eldar, <a href="/A095738/b095738.txt">Table of n, a(n) for n = 1..10000</a>
%H A095738 Claude W. Anderson and Dean Hickerson, <a href="http://www.jstor.org/stable/2318325">Advanced Problem 6020: Friendly Integers</a>, Amer. Math. Monthly, 1977, V84#1p65-6.
%H A095738 Walter Nissen, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;560ec1b3.0407">Primitive Friendly Integers and Exclusive Multiples</a>, 2004 post to NMBRTHRY mailing list
%t A095738 Select[Range[320], PrimeNu[#] > 1 && GCD[#, DivisorSigma[1, #]] == 1 &] (* _Amiram Eldar_, Jun 25 2019 *)
%o A095738 (PARI) isok(n) = (gcd(sigma(n), n) == 1) && (! isprime(n)) && (! (ispower(n, , &p) && isprime(p))); \\ _Michel Marcus_, Jan 24 2014
%Y A095738 Cf. A014567, A074902, A095739, A000203, A033880.
%K A095738 nonn
%O A095738 1,1
%A A095738 _Walter Nissen_, Jul 08 2004
%E A095738 Edited by _Franklin T. Adams-Watters_, Mar 06 2014