A285457 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.

3, 2, 6, 17, 12, 25, 24, 37, 48, 325, 60, 144, 120, 121, 168, 289, 180, 529, 240, 577, 481, 361, 360, 900, 960, 961, 721, 5185, 720, 841, 840, 2401, 1261, 17425, 1260, 14641, 1680, 1681, 2161, 8281, 2880, 3600, 6480, 7057, 2520, 6241, 2521, 82945, 6481, 225625, 7200

Offset: 0

Author

Paolo P. Lava, Apr 26 2017

Keywords

• nonn

Comments

Odd-indexed terms are equal to a square or to a square plus one. - Giovanni Resta, Apr 28 2017

Examples

			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.
		

Links

• Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 0..1000 (first 150 terms from Paolo P. Lava)

Crossrefs

Cf. A000005, A051950, A086550 (without abs), A285787 (with bigomega).

Programs

Maple

with(numtheory): P:=proc(q) local a,b,k,v; v:=array(0..200);
for k from 0 to 200 do v[k]:=0; od; a:=1;
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;
while v[k]>0 do print(v[k]); k:=k+1; od; print(); end: P(3*10^5);

Mathematica

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 *)

Formula

Least solutions of the equation abs(A000005(k) - A000005(k-1)) = n.