A133996 - OEIS

A133996

a(n) = the smallest positive integer with exactly n positive "non-isolated divisors". A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

%I #12 Oct 11 2017 21:58:07

%S 2,6,12,30,60,90,180,360,630,420,840,1680,4200,1260,2520,3780,7560,

%T 15120,13860,36960,49140,27720,32760,65520,83160,98280,196560,314160,

%U 277200,491400,526680,471240,360360,1164240,942480,720720,1081080

%N a(n) = the smallest positive integer with exactly n positive "non-isolated divisors". A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.

%H Ray Chandler, <a href="/A133996/b133996.txt">Table of n, a(n) for n=2..85</a>

%t With[{s = KeySort@ PositionIndex@ Table[1 + Count[Rest@ Divisors@ n, _?(AnyTrue[# + {-1, 1}, Divisible[n, #] &] &)], {n, 1200000}]}, Function[t, TakeWhile[#, # > 0 &] &@ Rest@ ReplacePart[t, Map[# -> Lookup[s, #][[1]] &, Keys@ s]]]@ ConstantArray[0, Last@ Keys@ s]] (* _Michael De Vlieger_, Oct 11 2017 *)

%Y Cf. A133997, A132747.

%K nonn

%O 2,1

%A _Leroy Quet_, Oct 01 2007

%E Extended by _Ray Chandler_, Jun 24 2008