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A055079 Smallest number with exactly n nonprime divisors. 9
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 (list; graph; refs; listen; history; text; internal format)
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} ];

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 A035403 A050908

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

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Last modified July 9 01:30 EDT 2020. Contains 335537 sequences. (Running on oeis4.)