A351549 - OEIS

%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&amp;name2=A351556&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;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