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A241648 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 3.

%I A241648 #21 Dec 19 2024 06:16:05
%S A241648 4,124,320,392,416,800,1352,1520,2912,2960,3536,3872,5720,5936,6320,
%T A241648 7112,8216,9176,9912,10472,11816,12152,12896,13280,14960,15176,16080,
%U A241648 16400,16536,18032,18392,18560,19136,19880,20000,21632,21680,21920,22736,23120,23816
%N A241648 Numbers m such that the GCD of the x's that satisfy sigma(x) = m is 3.
%H A241648 Amiram Eldar, <a href="/A241648/b241648.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..850 from Robert Israel)
%H A241648 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A241648 We have sigma(48) = sigma(75) = 124, and gcd(48, 75) = 3, hence 124 is in the sequence.
%e A241648 Likewise, we have sigma(x) = 2912 for x = [1116, 1236, 1701, 2007, 2181], with gcd 3.
%p A241648 N:= 10^5: # for terms <= N
%p A241648 V:= Vector(N):
%p A241648 for x from 1 to N do
%p A241648   s:= numtheory:-sigma(x);
%p A241648   if s <= N then
%p A241648     if V[s] = 0 then V[s]:= x
%p A241648     else V[s]:= igcd(V[s], x)
%p A241648     fi
%p A241648   fi
%p A241648 od: select(t -> V[t]=3, [$1..N]); # _Robert Israel_, Aug 18 2019
%o A241648 (PARI) is(k) = gcd(invsigma(k)) == 3; \\ _Amiram Eldar_, Dec 19 2024, using _Max Alekseyev_'s invphi.gp
%Y A241648 Cf. A000203, A240667, A241625, A241646, A241647, A241648, A241649, A241650.
%K A241648 nonn
%O A241648 1,1
%A A241648 _Michel Marcus_, Apr 26 2014