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A192290 Anti-amicable numbers. 4
14, 16, 92, 114, 5566, 6596, 1077378, 1529394, 3098834, 3978336, 70774930, 92974314 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Like A063990 but using anti-divisors. sigma*(a)=b and sigma*(b)=a, where sigma*(n) is the sum of  the anti-divisors of n. Anti-perfect numbers A073930 are not included in the sequence.

There are also chains of 3 or more anti-sociable numbers.

With 3 numbers the first chain is: 1494, 2056, 1856.

sigma*(1494) = 4+7+12+29+36+49+61+103+332+427+996 = 2056.

sigma*(2056) = 3+9+16+1371+457 = 1856.

sigma*(1856) = 3+47+79+128+1237 = 1494.

With 4 numbers the first chain is: 46, 58, 96, 64.

sigma*(46) = 3+4+7+13+31 = 58.

sigma*(58) = 3+4+5+9+13+23+39 = 96.

sigma*(96) = 64.

sigma*(64) = 3+43 = 46.

LINKS

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

EXAMPLE

sigma*(14) = 3+4+9 = 16; sigma*(16) = 3+11 = 14.

sigma*(92) = 3+5+8+37+61= 114; sigma*(114) = 4+12+76 = 92.

sigma*(5566) = 3+4+9+44+92+484+1012+1237+3711= 6596; sigma*(6596) = 3+8+79+136+776+167+4397 = 5566.

MAPLE

with(numtheory);

A192290 := proc(q)

local a, b, c, k, n;

for n from 1 to q do

  a:=0;

  for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;

  b:=a; c:=0;

  for k from 2 to b-1 do if abs((b mod k)-k/2)<1 then c:=c+k; fi; od;

  if n=c and not a=c then print(n); fi;

od; end:

A192290(1000000000);

PROG

(Python)

from sympy import divisors

def sigma_s(n):

....return sum([2*d for d in divisors(n) if n > 2*d and n % (2*d)] +

...........[d for d in divisors(2*n-1) if n > d >=2 and n % d] +

...........[d for d in divisors(2*n+1) if n > d >=2 and n % d])

A192290 = [n for n in xrange(1, 10**4) if sigma_s(n) != n and sigma_s(sigma_s(n)) == n] # Chai Wah Wu, Aug 14 2014

CROSSREFS

Cf. A063990, A066272, A192291, A192292, A192293.

Sequence in context: A224402 A067844 A015877 * A152010 A243750 A046085

Adjacent sequences:  A192287 A192288 A192289 * A192291 A192292 A192293

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Jun 29 2011

EXTENSIONS

a(7)-a(12) from Donovan Johnson, Sep 12 2011

STATUS

approved

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Last modified March 26 04:55 EDT 2017. Contains 284111 sequences.