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A241646 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 1.

%I A241646 #17 Dec 19 2024 06:15:56
%S A241646 1,12,18,24,31,32,42,48,54,56,60,72,80,84,90,96,98,104,108,114,120,
%T A241646 128,132,140,144,152,156,168,180,182,192,216,224,228,234,240,248,252,
%U A241646 264,270,272,280,288,294,308,312,324,336,342,360,372,384,390,408,420
%N A241646 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 1.
%H A241646 Robert Israel, <a href="/A241646/b241646.txt">Table of n, a(n) for n = 1..10000</a>
%H A241646 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A241646 We have sigma(6) = sigma(11) = 12, and gcd(6, 11) = 1, hence 12 is in the sequence.
%e A241646 For x in [20, 26, 41], sigma(x) = 42, and gcd(20, 26, 41) = 1, hence 42 is here.
%p A241646 N:= 10^4: # for terms <= N
%p A241646 V:= Vector(N):
%p A241646 for x from 1 to N do
%p A241646   s:= numtheory:-sigma(x);
%p A241646   if s <= N then
%p A241646     if V[s] = 0 then V[s]:= x
%p A241646     else V[s]:= igcd(V[s], x)
%p A241646     fi
%p A241646   fi
%p A241646 od: select(t -> V[t]=1, [$1..N]);  # _Robert Israel_, Aug 18 2019
%o A241646 (PARI) is(k) = gcd(invsigma(k)) == 1; \\ _Amiram Eldar_, Dec 19 2024, using _Max Alekseyev_'s invphi.gp
%Y A241646 Cf. A000203, A240667, A241625, A241646, A241647, A241648, A241649, A241650.
%K A241646 nonn
%O A241646 1,2
%A A241646 _Michel Marcus_, Apr 26 2014