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A192290 Anti-amicable numbers. 4

%I

%S 14,16,92,114,5566,6596,1077378,1529394,3098834,3978336,70774930,

%T 92974314

%N Anti-amicable numbers.

%C 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.

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

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

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

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

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

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

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

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

%C sigma*(96) = 64.

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

%C No other pairs with the larger term < 2147000000. - _Jud McCranie_ Sep 24 2019

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

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

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

%p with(numtheory);

%p A192290 := proc(q)

%p local a,b,c,k,n;

%p for n from 1 to q do

%p a:=0;

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

%p b:=a; c:=0;

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

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

%p od; end:

%p A192290(1000000000);

%o (Python)

%o from sympy import divisors

%o def sigma_s(n):

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

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

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

%o A192290 = [n for n in range(1,10**4) if sigma_s(n) != n and sigma_s(sigma_s(n)) == n] # _Chai Wah Wu_, Aug 14 2014

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

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Jun 29 2011

%E a(7)-a(12) from _Donovan Johnson_, Sep 12 2011

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Last modified March 8 00:38 EST 2021. Contains 341934 sequences. (Running on oeis4.)