

A247334


Highly abundant numbers which are not abundant.


0




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



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, n1, sign(sigma(n)sigma(i))) == n1) && (sigma(n) <= 2*n), print1(n, ", "))) \\ Michel Marcus, Sep 21 2014
(PARI) is_A247334(n)={!for(i=2, n1, sigma(n)>sigma(i)return) && sigma(n)<=2*n} \\ M. F. Hasler, Oct 15 2014


CROSSREFS



KEYWORD

fini,full,nonn


AUTHOR



STATUS

approved



