A130846 Replace n with the concatenation of its anti-divisors.

2, 3, 23, 4, 235, 35, 26, 347, 237, 58, 2359, 349, 2610, 311, 235711, 45712, 2313, 3813, 2614, 345915, 235915, 716, 2371017, 3417, 2561118, 3581119, 2319, 41220, 237921, 35791321, 2561322, 3423, 23101423, 824, 2351525, 3457111525, 2671126, 391627

Offset: 3

Author

Jonathan Vos Post, Jul 20 2007, Jul 22 2007

Keywords

• base
• easy
• nonn

Comments

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.

See A066272 for definition of anti-divisor.

Primes in this sequence are at n=3,4,5,10,14,16,40,46,100,145,149,... - R. J. Mathar, Jul 24 2007

Examples

			3: 2, so a(3) = 2.
4: 3, so a(4) = 3.
5: 2, 3, so a(5) = 23.
6: 4, so a(6) = 4.
7: 2, 3, 5, so a(7) = 235.
17: 2, 3, 5, 7, 11, so a(17) = 235711
		

Links

• Jon Perry, The Anti-Divisor, cached copy.
• Jonathan Vos Post, Factors of first 62 terms

Crossrefs

Cf. A037278, A066272, A120712, A106708, A130799.

Programs

Maple

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

Python

from sympy.ntheory.factor_ import antidivisors
def A130846(n): return int(''.join(str(s) for s in antidivisors(n))) # Chai Wah Wu, Dec 08 2021

Extensions

More terms from R. J. Mathar, Jul 24 2007