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%I #23 Feb 26 2024 02:01:00
%S 2,3,23,4,235,35,26,347,237,58,2359,349,2610,311,235711,45712,2313,
%T 3813,2614,345915,235915,716,2371017,3417,2561118,3581119,2319,41220,
%U 237921,35791321,2561322,3423,23101423,824,2351525,3457111525,2671126,391627
%N Replace n with the concatenation of its anti-divisors.
%C Number of anti-divisors concatenated to form a(n) is A066272(n). We may consider prime values of the concatenated anti-divisor sequence and we may iterate it, i.e. n, a(n), a(a(n)), a(a(a(n))) which leads to questions of trajectory, cycles, fixed points.
%C See A066272 for definition of anti-divisor.
%C Primes in this sequence are at n=3,4,5,10,14,16,40,46,100,145,149,... - _R. J. Mathar_, Jul 24 2007
%H Jon Perry, <a href="/A066272/a066272a.html">The Anti-Divisor</a>, cached copy.
%H Jonathan Vos Post, <a href="/A130846/a130846.txt">Factors of first 62 terms</a>
%e 3: 2, so a(3) = 2.
%e 4: 3, so a(4) = 3.
%e 5: 2, 3, so a(5) = 23.
%e 6: 4, so a(6) = 4.
%e 7: 2, 3, 5, so a(7) = 235.
%e 17: 2, 3, 5, 7, 11, so a(17) = 235711
%p antiDivs := proc(n) local resul,odd2n,r ; resul := {} ; for r in ( numtheory[divisors](2*n-1) union numtheory[divisors](2*n+1) ) do if n mod r <> 0 and r> 1 and r < n then resul := resul union {r} ; fi ; od ; odd2n := numtheory[divisors](2*n) ; for r in odd2n do if ( r mod 2 = 1) and r > 2 then resul := resul union {2*n/r} ; fi ; od ; RETURN(resul) ; end: A130846 := proc(n) cat(op(antiDivs(n))) ; end: seq(A130846(n),n=3..80) ; # _R. J. Mathar_, Jul 24 2007
%o (Python)
%o from sympy.ntheory.factor_ import antidivisors
%o def A130846(n): return int(''.join(str(s) for s in antidivisors(n))) # _Chai Wah Wu_, Dec 08 2021
%Y Cf. A037278, A066272, A120712, A106708, A130799.
%K base,easy,nonn
%O 3,1
%A _Jonathan Vos Post_, Jul 20 2007, Jul 22 2007
%E More terms from _R. J. Mathar_, Jul 24 2007
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