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A137205 Numbers k such that abundance(k) + abundance(k+1) = 2. 0
215, 923, 944, 1455, 2379, 5355, 6467, 6623, 14099, 23495, 196343, 212795, 1661135, 4070199, 4160919, 4626699, 60464627, 217408415, 248621603, 262792907, 265371335, 613033667, 684241907, 1065360113, 3148946723, 4773647871, 6729842063, 19910536424 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The abundance of k is defined as the difference between the sum of the aliquot parts of k and k itself.

LINKS

Table of n, a(n) for n=1..28.

FORMULA

{k: A033880(k) + A033880(k+1) = 2}. - R. J. Mathar, Apr 01 2008

EXAMPLE

abundance(215) = (sum of aliquot parts of 215) - 215 = 49 - 215 = -166;

abundance(216) = (sum of aliquot parts of 216) - 216 = 384 -216 = 168;

so abundance(215) + abundance(216) = 2.

MAPLE

with(numtheory): a:=proc(n) if sigma(n)+sigma(n+1)-4*n=4 then n end if end proc: seq(a(n), n=1..100000); # Emeric Deutsch, Apr 02 2008

MATHEMATICA

Select[Range[10^6], DivisorSigma[1, #] + DivisorSigma[1, # + 1] - 4 # == 4 &] (* Michael De Vlieger, Feb 02 2019 *)

CROSSREFS

Cf. A033880.

Sequence in context: A193398 A193396 A259889 * A091289 A085754 A232252

Adjacent sequences:  A137202 A137203 A137204 * A137206 A137207 A137208

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Mar 04 2008

EXTENSIONS

Three more terms from R. J. Mathar and Emeric Deutsch, Apr 01 2008

a(14)-a(28) from Donovan Johnson, Apr 27 2008

STATUS

approved

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Last modified January 26 20:42 EST 2020. Contains 331288 sequences. (Running on oeis4.)