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%I #21 Dec 11 2019 06:49:09
%S 3,2,6,17,12,25,24,37,48,325,60,144,120,121,168,289,180,529,240,577,
%T 481,361,360,900,960,961,721,5185,720,841,840,2401,1261,17425,1260,
%U 14641,1680,1681,2161,8281,2880,3600,6480,7057,2520,6241,2521,82945,6481,225625,7200
%N Least number k such that the absolute value of the difference between the number of divisors of k and k-1 is equal to n.
%C Odd-indexed terms are equal to a square or to a square plus one. - _Giovanni Resta_, Apr 28 2017
%H Paolo P. Lava and Giovanni Resta, <a href="/A285457/b285457.txt">Table of n, a(n) for n = 0..1000</a> (first 150 terms from Paolo P. Lava)
%F Least solutions of the equation abs(A000005(k) - A000005(k-1)) = n.
%e a(9) = 325 because 324 has 15 divisors (1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324), 325 has 6 divisors (1, 5, 13, 25, 65, 325) and 15 - 6 = 9.
%p with(numtheory): P:=proc(q) local a,b,k,v; v:=array(0..200);
%p for k from 0 to 200 do v[k]:=0; od; a:=1;
%p for k from 2 to q do b:=tau(k); if v[abs(b-a)]=0 then v[abs(b-a)]:=k; fi; a:=b; od; k:=0;
%p while v[k]>0 do print(v[k]); k:=k+1; od; print(); end: P(3*10^5);
%t s = DivisorSigma[0, #] &@ Range[10^6]; 1 + First /@ Values@ KeySort@ PositionIndex@ Flatten@ Map[Abs@ Differences@ # &, Partition[s, 2, 1]] (* _Michael De Vlieger_, Apr 26 2017, Version 10 *)
%Y Cf. A000005, A051950, A086550 (without abs), A285787 (with bigomega).
%K nonn
%O 0,1
%A _Paolo P. Lava_, Apr 26 2017
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