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A223610 Numbers k whose abundance is 18: sigma(k) - 2*k = 18. 2
208, 6976, 8415, 31815, 351351, 2077696, 20487159, 159030135, 536559616, 2586415095, 137433972736, 2199003332608 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Suggested by N. J. A. Sloane and Robert G. Wilson v.

a(12) > 10^12.

a(13) > 10^13. - Giovanni Resta, Mar 29 2013

a(13) > 10^18. - Hiroaki Yamanouchi, Aug 23 2018

Any term x of this sequence can be combined with any term y of A223608 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016

a(13) <= 2305842988812599296. Every number of the form 2^(j-1)*(2^j - 19), where 2^j - 19 is prime, is a term. - Jon E. Schoenfield, Jun 02 2019

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

For k = 159030135, sigma(k) - 2*k = 18.

MATHEMATICA

Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 18 &] (* Vincenzo Librandi, Sep 14 2016 *)

PROG

(PARI) for(n=1, 10^8, if(sigma(n)-2*n==18, print1(n ", ")))

(MAGMA) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 18]; // Vincenzo Librandi, Sep 14 2016

CROSSREFS

Cf. A000203, A033880, A223608 (deficiency 18).

Sequence in context: A172967 A231111 A223252 * A184276 A268091 A209300

Adjacent sequences:  A223607 A223608 A223609 * A223611 A223612 A223613

KEYWORD

nonn,more

AUTHOR

Donovan Johnson, Mar 23 2013

EXTENSIONS

a(12) from Giovanni Resta, Mar 29 2013

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)