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The n-th highly composite number equals the a(n)-th composite number, for n >= 3.
1

%I #16 Aug 18 2024 05:18:10

%S 0,0,1,2,6,14,24,32,42,89,138,187,287,591,693,1054,1416,2151,4364,

%T 6600,8842,13354,17879,22418,24697,40653,45227,49811,75040,100357,

%U 151121,202000,252981,304025,457506,508744,611307,662636,996722,1331409

%N The n-th highly composite number equals the a(n)-th composite number, for n >= 3.

%C Since the first 2 highly composite numbers, 1 and 2, are not composite numbers, the first 2 terms here were taken to be 0.

%H Amiram Eldar, <a href="/A074329/b074329.txt">Table of n, a(n) for n = 1..217</a>

%F a(n) = A002182(n) - A000720(A002182(n)) - 1.

%F A002808(a(n)) = A002182(n).

%e The 6th highly composite number is 24, the 14th composite number, so a(6) = 14.

%t t[x_] := A002182[x]; Table[Part[t, w]-PrimePi[Part[t, w]]-1, {w, 1, Length[t]}]

%Y Cf. A002182, A002808, A000720.

%K nonn

%O 1,4

%A _Labos Elemer_, Aug 21 2002