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A247334 Highly abundant numbers which are not abundant. 0
1, 2, 3, 4, 6, 8, 10, 16 (list; graph; refs; listen; history; text; internal format)
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
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 A372032
KEYWORD
fini,full,nonn
AUTHOR
Andrew Rodland, Sep 13 2014
STATUS
approved

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Last modified July 21 12:25 EDT 2024. Contains 374472 sequences. (Running on oeis4.)