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

Author

Antti Karttunen, Feb 19 2022

Keywords

• nonn
• more
• changed

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

• 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

Crossrefs

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

Subsequence of A386424.

Cf. also A351458, A351548.

Programs

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)); };