A336565 - OEIS

%I #14 Aug 06 2020 22:04:40

%S 6,28,234,496,588,600,1521,1638,6552,8128,55860,89376,33550336,

%T 168836850

%N Numbers k for which (A057723(k)-k) is equal to gcd(k-A308135(k), A057723(k)-k).

%C Numbers k for which A336563(k) = A336566(n) [= gcd(A336563(n), A336564(n))].

%C Numbers k such that either both A336563(k) and A336564(k) are zero (in which case k is squarefree), or A336563(k) divides A336564(k), in which case k is not squarefree.

%C Also numbers k for which A336647(n) = 2*n - A057723(n).

%C Question: Are there any other odd terms apart from 1521 = 39^2 ?

%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 A007947(n) = factorback(factorint(n)[, 1]);

%o A057723(n) = { my(r=A007947(n)); (r*sigma(n/r)); };

%o isA336565(n) = { my(b=A057723(n), c=(sigma(n)-b), d=(b-n)); (gcd(d,(n-c))==d); };

%Y Cf. A057723, A308135, A336563, A336564, A336566, A336647.

%Y Cf. A000396 (a subsequence).

%Y Cf. also A326145.

%K nonn,more

%O 1,1

%A _Antti Karttunen_, Jul 26 2020