A172442 A sixth of the smallest integer for which the number of divisors is the n-th composite.

1, 2, 4, 6, 8, 10, 32, 24, 20, 30, 40, 96, 512, 60, 216, 2048, 150, 160, 120, 140, 1536, 32768, 864, 210, 131072, 6144, 280, 480, 2560, 600, 2097152, 420, 7776, 1080, 98304, 10240, 1050, 13824, 1120, 393216, 134217728, 840, 536870912, 2400, 1260, 55296, 7680, 163840, 6291456

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 12 2011

Keywords

• nonn
• less

Examples

			The first composite is A002808(1)=4. The smallest integer with 4 divisors is A005179(4) = 6, which divided by 6 yields a(1)=1.
		

Crossrefs

Cf. A002808, A005179, A061286, A187678.

Programs

Mathematica

nd[n_]:=Module[{k=6},While[DivisorSigma[0,k]!=n,k+=6];k]; With[{cmps=Select[Range[45],CompositeQ]},(Table[nd[c],{c,cmps}])/6] (* The program generates the first 30 terms of the sequence. *) (* Harvey P. Dale, Jun 15 2025 *)

Formula

a(n) = A005179(A002808(n))/6.