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A241647 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 2.

%I A241647 #21 Dec 19 2024 06:16:00
%S A241647 3,126,186,399,924,1350,1386,1530,1806,2106,2646,2652,2814,2916,3066,
%T A241647 3150,3654,3870,4662,4914,6162,6426,6846,6882,6930,7098,7566,7620,
%U A241647 8190,8910,9270,10842,11076,12222,12870,14586,14910,15210,15246,15930,16506,17010
%N A241647 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 2.
%H A241647 Amiram Eldar, <a href="/A241647/b241647.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1849 from Robert Israel)
%H A241647 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A241647 We have sigma(68) = sigma(82) = 126, and gcd(68, 82) = 2, hence 126 is in the sequence.
%e A241647 On the other hand, for x in [20, 26, 41], sigma(x) = 42, and gcd(20, 26, 41) = 1, hence 42 is not here, although gcd(20, 26) is 2.
%p A241647 N:= 10^5: # for terms <= N
%p A241647 V:= Vector(N):
%p A241647 for x from 1 to N do
%p A241647   s:= numtheory:-sigma(x);
%p A241647   if s <= N then
%p A241647     if V[s] = 0 then V[s]:= x
%p A241647     else V[s]:= igcd(V[s], x)
%p A241647     fi
%p A241647   fi
%p A241647 od: select(t -> V[t]=2, [$1..N]); # _Robert Israel_, Aug 18 2019
%o A241647 (PARI) is(k) = gcd(invsigma(k)) == 2; \\ _Amiram Eldar_, Dec 19 2024, using _Max Alekseyev_'s invphi.gp
%Y A241647 Cf. A000203, A240667, A241625, A241646, A241647, A241648, A241649, A241650.
%K A241647 nonn
%O A241647 1,1
%A A241647 _Michel Marcus_, Apr 26 2014