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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Prog

(PARI) sme(n) = {k = 1; while (sumdiv(k, d, ! isprime(d)) != n, k++); k; } \\ Michel Marcus, Dec 13 2013
(Haskell)
a055079 n = head [x | x <- [1..], a033273 x == n]
-- Reinhard Zumkeller, Dec 16 2013

Crossrefs

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

Sequence in context: A233341 A102110 A302829 * A081833 A370134 A035403

Adjacent sequences: A055076 A055077 A055078 * A055080 A055081 A055082

Keyword

nonn,nice

Author

Labos Elemer, Jun 13 2000

Extensions

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

Edited by Ray Chandler, Aug 12 2010

Status

approved