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A319865 Product of distinct prime factors of highly composite numbers (definition 1, A002182).

%I A319865 #32 Feb 16 2025 08:33:56
%S A319865 1,2,2,6,6,6,6,6,30,30,30,30,30,30,210,210,210,210,210,210,210,210,
%T A319865 210,210,2310,210,210,2310,2310,2310,2310,2310,2310,2310,2310,2310,
%U A319865 2310,30030,30030,30030,30030,30030,30030,30030,30030,30030,30030,30030,30030,30030,30030,30030,510510,30030
%N A319865 Product of distinct prime factors of highly composite numbers (definition 1, A002182).
%H A319865 Amiram Eldar, <a href="/A319865/b319865.txt">Table of n, a(n) for n = 1..10000</a>
%H A319865 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly Composite Number</a>
%H A319865 Wikipedia, <a href="http://www.wikipedia.org/wiki/Highly_composite_number">Highly composite number</a>
%F A319865 a(n) = A007947(A002182(n)). - _Michel Marcus_, Sep 30 2018
%e A319865 n  | A002182(n)                       | a(n)
%e A319865 ---+----------------------------------+--------------------------
%e A319865 24 | 25200 = 2^4 * 3^2 * 5^2 * 7      |  210 = 2 * 3 * 5 * 7
%e A319865 25 | 27720 = 2^3 * 3^2 * 5   * 7 * 11 | 2310 = 2 * 3 * 5 * 7 * 11
%e A319865 26 | 45360 = 2^4 * 3^4 * 5   * 7      |  210 = 2 * 3 * 5 * 7
%e A319865 27 | 50400 = 2^5 * 3^2 * 5^2 * 7      |  210 = 2 * 3 * 5 * 7
%Y A319865 Cf. A002182, A007947, A108602, A112779, A272605.
%K A319865 nonn
%O A319865 1,2
%A A319865 _Seiichi Manyama_, Sep 29 2018