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
Keywords
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)
Programs
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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);
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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 *)
Comments