A185078 Numbers k for which A064380(k) = k/2.

2, 6, 8, 10, 60, 70, 128, 136, 9822, 18632, 32768, 32896, 36720, 69726, 73662, 73686, 73734, 85962, 86046, 87114, 87198, 87222, 87258, 87294, 87306, 87342, 87366, 87546, 87558, 88014, 88278, 88302, 88338, 88386, 127326, 128046, 128082, 128382, 128406, 128598, 128802

Offset: 1

Author

Vladimir Shevelev, Feb 18 2011

Keywords

• nonn

Comments

Note that, if there exist infinitely many infinitary perfect numbers (A007357), then, as k tends to infinity over such numbers, A064380(k)/k = 1/2 + o(k^(-1+eps)). We conjecture that here A064380(k)/k = 1/2 infinitely many times, and thus the sequence contains infinitely many infinitary perfect numbers.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..201

Crossrefs

Cf. A064380, A007357, A064380, A185373, A185383.

Extensions

a(7)-a(13) from Amiram Eldar, Sep 13 2019

a(14)-a(41) from Amiram Eldar, Mar 26 2023