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 A163816 Integers with exactly 100 divisors. 1
 45360, 71280, 84240, 99792, 110160, 117936, 123120, 149040, 154224, 162000, 172368, 185328, 187920, 200880, 207360, 208656, 210000, 239760, 242352, 263088, 265680, 270000, 270864, 278640, 281232, 286416, 290304, 304560, 320112, 327888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Zak Seidov, Aug 07 2009: (Start) Numbers n with A000005(n)=tau(n)=100. a(1)=45360 because 45360=2^4*3^4*5^1*7^1 and tau(45360)=A000005(45360)=(4+1)(4+1)(1+1)(1+1)=100. First odd term is a(536)=3898125=3^4*5^4*5^7*1^1. (End) These are numbers with prime signatures {99}, {49,1}, {24,3}, {19,4}, {9,9}, {24,1,1}, {9,4,1}, {4,4,3}, and {4,4,1,1}. - T. D. Noe, May 09 2011 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE a(1)=45360 which is divisible by exactly 100 factors:(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 70, 72, 80, 81, 84, 90, 105, 108, 112, 120, 126, 135, 140, 144, 162, 168, 180, 189, 210, 216, 240, 252, 270, 280, 315, 324, 336, 360, 378, 405, 420, 432, 504, 540, 560, 567, 630, 648, 720, 756, 810, 840, 945, 1008, 1080, 1134, 1260, 1296, 1512, 1620, 1680, 1890, 2160, 2268, 2520, 2835, 3024, 3240, 3780, 4536, 5040, 5670, 6480, 7560, 9072, 11340, 15120, 22680, 45360) MATHEMATICA S={}; Do[If[DivisorSigma[0, n]==100, AppendTo[S, n]], {n, 45360, 10^7}]; S (* Zak Seidov, Aug 07 2009 *) CROSSREFS Cf. A000005. Sequence in context: A031851 A185927 A287378 * A055355 A210618 A269936 Adjacent sequences: A163813 A163814 A163815 * A163817 A163818 A163819 KEYWORD easy,nonn AUTHOR Gil Broussard, Aug 04 2009 STATUS approved

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Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)