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

1,1

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

Table of n, a(n) for n=1..14.

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

Prog

(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); };

Crossrefs

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

Cf. A000396 (a subsequence).

Cf. also A326145.

Sequence in context: A034660 A347770 A206708 * A216413 A090898 A134872

Adjacent sequences: A336562 A336563 A336564 * A336566 A336567 A336568

Keyword

nonn,more

Author

Antti Karttunen, Jul 26 2020

Status

approved