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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Andrew Rodland

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A247334 Highly abundant numbers which are not abundant.

Original entry on oeis.org

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

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Author

Andrew Rodland, Sep 13 2014

Keywords

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.

Examples

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

Links

Crossrefs

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

Programs

  • 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

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