A256605 Least k such that n+1 is the n-th divisor of k.

3, 4, 20, 12, 84, 120, 360, 360, 3960, 2520, 32760, 27720, 27720, 55440, 942480, 720720, 13693680, 12252240, 12252240, 12252240, 281801520, 232792560, 1163962800, 1163962800, 3491888400, 3491888400, 101264763600, 80313433200, 2489716429200, 4658179125600

Offset: 2

Author

Michel Lagneau, Apr 04 2015

Keywords

• nonn
• easy

Comments

The case n = 1 is not possible because the number 2 is never the first divisor of k (1 is the first divisor).

Examples

			a(6) = 84 because the divisors of 84 are {1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84} and 7 is the 6th divisor of 84.
		

Crossrefs

Cf. A003418, A007917, A225562.

See A221647 for other sequences giving the smallest number whose n-th divisor satisfies some condition.

Programs

Maple

with(numtheory):for n from 2 to 31 do:ii:=0:for  k from 1 to 10^9 while(ii=0) do:x:=divisors(k):n1:=nops(x):if n<=n1 and x[n]=n+1 then ii:=1: printf ( "%d %d \n",n,k):else fi:od:od:

Mathematica

nn=20;t=Table[0,{nn}];found=1;n=2;While[found
				

PARI

a(n) = {k = 1; ok = 0; while (!ok, d = divisors(k); if ((#d >= n) && (d[n] == n+1), ok = 1, k++);); k;} \\ Michel Marcus, Apr 04 2015

Formula

a(n) = A003418(n+1)/A007917(n). - Peter Munn, May 14 2025