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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. No other pairs with the larger term < 2147000000. - Jud McCranie Sep 24 2019 LINKS 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 range(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 A352381 A243750 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 29 11:38 EDT 2023. Contains 361599 sequences. (Running on oeis4.)