A351549 Numbers k for which k * gcd(sigma(k), A019565(k)) is equal to sigma(k) * gcd(k, A019565(k)).

1, 1456, 15480, 114660, 2244600, 3894768, 25108200, 27052704, 65021040, 112402080, 1973921400

Offset

1,2

Comments

Numbers k such that their abundancy index [sigma(k)/k] is equal to A351557(k)/A351556(k).

Question: If the above ratio is neither 1 nor 2, must it then be > 2? Are all even terms abundant?

a(12) > 2281701376 if it exists.

Links

Table of n, a(n) for n=1..11.

Antti Karttunen, Ratio A351557(n)/A351556(n) plotted with OEIS Plot2 tool

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

Prog

(PARI)
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
isA351549(n) = { my(s=sigma(n), z=A019565(n)); (n*gcd(s, z))==(s*gcd(n, z)); };

Crossrefs

Cf. A000203, A005101, A007947, A019565, A080398, A351556, A351557, A351558, A351559.

Cf. also A351458, A351548.

Sequence in context: A145529 A203393 A235771 * A235554 A255345 A091715

Adjacent sequences: A351546 A351547 A351548 * A351550 A351551 A351552

Keyword

nonn,more

Author

Antti Karttunen, Feb 19 2022

Status

approved