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%I #22 Feb 20 2022 08:38:32
%S 1,1456,15480,114660,2244600,3894768,25108200,27052704,65021040,
%T 112402080,1973921400
%N Numbers k for which k * gcd(sigma(k), A019565(k)) is equal to sigma(k) * gcd(k, A019565(k)).
%C Numbers k such that their abundancy index [sigma(k)/k] is equal to A351557(k)/A351556(k).
%C Question: If the above ratio is neither 1 nor 2, must it then be > 2? Are all even terms abundant?
%C a(12) > 2281701376 if it exists.
%H Antti Karttunen, <a href="https://oeis.org/plot2a?name1=A351557&name2=A351556&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawlines=true">Ratio A351557(n)/A351556(n) plotted with OEIS Plot2 tool</a>
%H <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%o (PARI)
%o A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o isA351549(n) = { my(s=sigma(n), z=A019565(n)); (n*gcd(s,z))==(s*gcd(n,z)); };
%Y Cf. A000203, A005101, A007947, A019565, A080398, A351556, A351557, A351558, A351559.
%Y Cf. also A351458, A351548.
%K nonn,more
%O 1,2
%A _Antti Karttunen_, Feb 19 2022
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