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Search: id:A055079
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| A055079 |
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Smallest number with n nonprime divisors. |
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+0
6
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| 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
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OFFSET
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1,2
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COMMENT
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a(n)<=2^n and in several cases this "least number" is equal to a(n). Such "nasty cases" are given in a separate sequence, A057838.
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FORMULA
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a(n)=Min{k; A000005(k)-A001221(k)=A033273(k)=n}
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EXAMPLE
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For example, a(35) = 2^35 = 34359738368 and a(71) = 2^71 = 2361183241434822606848. The next "nasty case" is n = 191: a(191) = 3138550867693340381917894711603833208051177722232017256448.
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).
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MATHEMATICA
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a = Table[0, {100} ]; Do[ c = Count[ PrimeQ[ Divisors[ n ] ], False]; If[ c < 101 && a[[ c ]] == 0, a[[ c ]] = n], {n, 2, 10077696} ];
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CROSSREFS
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Cf. A001221, A001222, A058060, A058061, A000005, A033273, A057838.
Sequence in context: A059992 A050570 A102110 this_sequence A081833 A035403 A050908
Adjacent sequences: A055076 A055077 A055078 this_sequence A055080 A055081 A055082
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KEYWORD
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nonn,nice
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 13 2000
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 20 2000
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