Definition:Highly Abundant Number/Examples
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Examples of Highly Abundant Numbers
The divisor sum values of the first few highly abundant numbers can be tabulated as:
$n$ $\map {\sigma_1} n$ Difference from previous peak $1$ $1$ $2$ $3$ $2$ $3$ $4$ $1$ $4$ $7$ $3$ $6$ $12$ $5$ $8$ $15$ $3$ $10$ $18$ $3$ $12$ $28$ $10$ $16$ $31$ $3$ $18$ $39$ $8$ $20$ $42$ $3$ $24$ $60$ $18$ $30$ $72$ $12$ $36$ $91$ $19$ $42$ $96$ $5$ $48$ $124$ $28$ $60$ $168$ $44$ $72$ $195$ $27$ $84$ $224$ $29$ $90$ $234$ $10$ $96$ $252$ $18$ $108$ $280$ $28$ $120$ $360$ $80$
Thus the sequence of peak divisor sums begins:
- $1, 3, 4, 7, 12, 15, 18, 28, 31, 39, 42, 60, 72, 91, 96, 124, 168, 195, 224, 234, 252, 280, 360, \ldots$
This sequence is A034885 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).