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 A163816 Integers with exactly 100 divisors. 1

%I #12 Mar 14 2023 03:39:56

%S 45360,71280,84240,99792,110160,117936,123120,149040,154224,162000,

%T 172368,185328,187920,200880,207360,208656,210000,239760,242352,

%U 263088,265680,270000,270864,278640,281232,286416,290304,304560,320112,327888

%N Integers with exactly 100 divisors.

%C From _Zak Seidov_, Aug 07 2009: (Start)

%C Numbers n with A000005(n)=tau(n)=100.

%C 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.

%C First odd term is a(536)=3898125=3^4*5^4*5^7*1^1. (End)

%C 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

%H T. D. Noe, <a href="/A163816/b163816.txt">Table of n, a(n) for n = 1..1000</a>

%e 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)

%t S={}; Do[If[DivisorSigma[0,n]==100,AppendTo[S,n]],{n,45360,10^7}]; S (* _Zak Seidov_, Aug 07 2009 *)

%Y Cf. A000005.

%K easy,nonn

%O 1,1

%A _Gil Broussard_, Aug 04 2009

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Last modified August 4 17:59 EDT 2024. Contains 374923 sequences. (Running on oeis4.)