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A034090 Numbers n such that sum of proper divisors of n exceeds that of all smaller numbers. 14
1, 2, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 48, 60, 72, 84, 90, 96, 108, 120, 144, 168, 180, 216, 240, 288, 300, 336, 360, 420, 480, 504, 540, 600, 660, 720, 840, 960, 1008, 1080, 1200, 1260, 1440, 1560, 1680, 1980, 2100, 2160, 2340, 2400, 2520, 2880, 3120, 3240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The highly abundant numbers A002093 are a subsequence since if sigma(n) - n > sigma(m) - m for all m < n then sigma(n) > sigma(m). - Charles R Greathouse IV, Sep 13 2016

LINKS

T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 372 terms from T. D. Noe)

EXAMPLE

Contribution from William A. Tedeschi, Aug 19 2010: (Start)

-- 12: 1+2+3+4+6 = 16

13: 1 = 1

14: 1+2+7 = 10

15: 1+3+5 = 9

16: 1+2+4+8 = 16

17: 1 = 1

-- 18: 1+2+3+6+9 = 21

As 12 had the previous (earliest) highest it is listed, then since 18 has the new highest, it is listed. (End)

MATHEMATICA

A={}; m=-1; For[ i=1, i<10000, i++, t=Apply[ Plus, Divisors[ i ] ]-i; If[ t>m, m=t; AppendTo[ A, i ] ] ]; A

PROG

(PARI) r=0; for(n=1, 1e6, t=sigma(n)-n; if(t>r, r=t; print1(n", "))) \\ Charles R Greathouse IV, Sep 13 2016

CROSSREFS

Supersequence of A002093.

Cf. A001065, A034091, A034287, A034288.

Sequence in context: A100180 A258137 A101814 * A146344 A162763 A113242

Adjacent sequences:  A034087 A034088 A034089 * A034091 A034092 A034093

KEYWORD

nonn,nice

AUTHOR

J. Lowell

EXTENSIONS

More terms from Erich Friedman

STATUS

approved

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Last modified February 22 12:33 EST 2020. Contains 332136 sequences. (Running on oeis4.)