cp's OEIS Frontend

A241481 Numbers such that the GCD of the x's that satisfy sigma(x) = sigma(n) is not equal to 1 while the number of such x's is not 1 either.

%I A241481 #18 May 28 2025 01:12:12
%S A241481 48,68,75,80,82,104,116,122,144,156,160,189,196,212,225,237,242,273,
%T A241481 279,291,309,328,342,356,364,403,490,513,524,531,592,597,614,640,651,
%U A241481 679,684,688,712,784,788,804,808,810,822,833,889,898,903,922,925,927,954
%N A241481 Numbers such that the GCD of the x's that satisfy sigma(x) = sigma(n) is not equal to 1 while the number of such x's is not 1 either.
%C A241481 Subsequence of A241480, restricted to those terms that do not belong to A211656.
%C A241481 Is it possible, for each term of A211656, to find a corresponding term in the present sequence such that the corresponding GCD is equal to the initial A211656 term?
%C A241481 The first 11 terms of A211656 are: 2, 3, 4, 5, 7, 8, 9, 12, 13, 18, 19.
%C A241481 For these, we have 68, 48, 104, 12735, 364, 7848, 144, 9984, 273, 1764, 1197 in the present sequence.
%C A241481 For instance for m = 9984, the x's are [9984, 12252], with gcd = 12.
%C A241481 Is it possible to find a term here with corresponding gcd = 22, the 12th term of A211656?
%H A241481 Robert Israel, <a href="/A241481/b241481.txt">Table of n, a(n) for n = 1..10000</a>
%H A241481 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%e A241481 48 is in the sequence because sigma(48)=124 and the x's such that sigma(x) = 124 are 48 and 75, with gcd(48, 75) not equal to 1.
%p A241481 M:=1000: # to get all terms <= M
%p A241481 N:= 0:
%p A241481 for n from 1 to M do
%p A241481   v:= numtheory:-sigma(n);
%p A241481   N:= max(N,v);
%p A241481   if assigned(R[v]) then R[v]:= igcd(R[v],n); S[v]:= S[v] union {n}
%p A241481   else R[v]:= n; S[v]:= {n}
%p A241481   fi;
%p A241481 od:
%p A241481 for n from M+1 to N do
%p A241481   v:= numtheory:-sigma(n);
%p A241481   if assigned(R[v]) then R[v]:= igcd(R[v],n);  S[v]:= S[v] union {n} fi;
%p A241481 od:
%p A241481 A:=
%p A241481 `union`(seq(S[v], v = select(t -> R[t]>1 and nops(S[t])>1, map(op,[indices(R)])))) intersect {$1..M}:
%p A241481 sort(convert(A,list)); # _Robert Israel_, Oct 24 2019
%o A241481 (PARI) sigv(n) =  select(i->sigma(i) == n, vector(n, i, i));
%o A241481 isok(n) = my(v = sigv(sigma(n))); ((gcd(v)!=1) && (#v != 1));
%o A241481 (PARI) isok(k) = my(v = invsigma(sigma(k))); #v > 1 && gcd(v) > 1; \\ _Amiram Eldar_, May 28 2025, using _Max Alekseyev_'s invphi.gp (see links).
%Y A241481 Cf. A000203, A211656, A241479, A241480.
%K A241481 nonn
%O A241481 1,1
%A A241481 _Michel Marcus_, Apr 23 2014