A336565 Numbers k for which (A057723(k)-k) is equal to gcd(k-A308135(k), A057723(k)-k).

6, 28, 234, 496, 588, 600, 1521, 1638, 6552, 8128, 55860, 89376, 33550336, 168836850

Offset: 1

Author

Antti Karttunen, Jul 26 2020

Keywords

• nonn
• more

Comments

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

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.

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

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

Links

• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

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

Cf. A000396 (a subsequence).

Cf. also A326145.

Programs

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A057723(n) = { my(r=A007947(n)); (r*sigma(n/r)); };
isA336565(n) = { my(b=A057723(n), c=(sigma(n)-b), d=(b-n)); (gcd(d,(n-c))==d); };