A055079 Smallest number with exactly n nonprime divisors.

1, 4, 8, 12, 30, 24, 36, 48, 60, 72, 2048, 192, 120, 216, 180, 288, 240, 432, 576, 420, 360, 864, 1296, 900, 960, 1728, 720, 840, 1080, 3456, 9216, 1260, 1440, 6912, 34359738368, 1680, 2160, 10368, 2880, 15552, 15360, 3600, 4620, 2520, 4320, 31104

Offset: 1

Author

Labos Elemer, Jun 13 2000

Keywords

• nonn
• nice

Comments

a(n)<=2^n; see A057838 for the indices n where a(n)=2^n.

Examples

			a(5) = 30 because it is the first integer which has five nonprime divisors (1, 6, 10, 15 and 30; the divisors 2, 3 and 5 are prime).
a(35) = 2^35 = 34359738368.
a(71) = 2^71 = 2361183241434822606848.
a(191) = 2^191 = 3138550867693340381917894711603833208051177722232017256448.
		

Links

• Ray Chandler, Table of n, a(n) for n=1..4438

Crossrefs

Cf. A001221, A001222, A058060, A058061, A000005, A033273, A057838.

Programs

Haskell

a055079 n = head [x | x <- [1..], a033273 x == n]
-- Reinhard Zumkeller, Dec 16 2013

Mathematica

a = Table[0, {100} ]; Do[ c = Count[ PrimeQ[ Divisors[ n ] ], False]; If[ c < 101 && a[[ c ]] == 0, a[[ c ]] = n], {n, 2, 10077696} ];
Table[SelectFirst[Table[{n,Count[Divisors[n],?(!PrimeQ[#]&)]},{n,10000}],#[[2]]==k&],{k,34}][[;;,1]] (* The program generates the first 34 terms of the sequence. *) (* _Harvey P. Dale, Mar 04 2024 *)

PARI

sme(n) = {k = 1; while (sumdiv(k, d, ! isprime(d)) != n, k++); k;} \\ Michel Marcus, Dec 13 2013

Formula

a(n)=Min{k; A000005(k)-A001221(k)=A033273(k)=n}

Extensions

More terms from Robert G. Wilson v, Nov 20 2000

Edited by Ray Chandler, Aug 12 2010