A247334 Highly abundant numbers which are not abundant.

1, 2, 3, 4, 6, 8, 10, 16

Offset

1,2

Comments

A number n is called "abundant" if sigma(n) > 2n, and "highly abundant" if sigma(n) > sigma(m) for all m < n. With these definitions, it's possible for a number to be highly abundant but not abundant. (A similar situation occurs with 2 being prime and highly composite.)

Fischer shows that all highly abundant numbers greater than 20 are multiples of 6. Since 6 is perfect and multiples of perfect numbers are abundant, this list is finite and complete.

Links

Table of n, a(n) for n=1..8.

Daniel Fischer, Prove that if Fn is highly abundant, then so is n, Mathematics Stack Exchange, Aug 13 2013

Example

10 is in the sequence because sigma(10) > sigma(m) for m = 1 to 9, yet sigma(10) = 17 < 20.

Prog

(PARI) for(n=1, 1000, if((sum(i=1, n-1, sign(sigma(n)-sigma(i))) == n-1) && (sigma(n) <= 2*n), print1(n, ", "))) \\ Michel Marcus, Sep 21 2014
(PARI) is_A247334(n)={!for(i=2, n-1, sigma(n)>sigma(i)||return) && sigma(n)<=2*n} \\ M. F. Hasler, Oct 15 2014

Crossrefs

Members of A002093 not in A005101. Members of A002093 in (A000396 union A005100).

Sequence in context: A238876 A211856 A066816 * A237450 A165514 A182417

Adjacent sequences: A247331 A247332 A247333 * A247335 A247336 A247337

Keyword

fini,full,nonn

Author

Andrew Rodland, Sep 13 2014

Status

approved