cp's OEIS Frontend

A181809 Numbers n such that both n and n/2 are highly composite (A002182).

%I A181809 #9 Feb 16 2025 08:33:13
%S A181809 2,4,12,24,48,120,240,360,720,1680,2520,5040,10080,15120,20160,50400,
%T A181809 55440,110880,166320,221760,332640,554400,665280,1441440,2162160,
%U A181809 2882880,4324320,7207200,8648640,14414400,17297280,21621600,43243200,73513440
%N A181809 Numbers n such that both n and n/2 are highly composite (A002182).
%C A181809 These are the numbers that set records both for total number of divisors and for number of even divisors; intersection of A002182 and A181808.
%C A181809 For all positive integer values (j,k) such that jk = n, the number of divisors of n that are multiples of j equals A000005(k). Therefore, n sets a record for the number of its divisors that are multiples of j iff k=n/j is highly composite (A002182).
%H A181809 Amiram Eldar, <a href="/A181809/b181809.txt">Table of n, a(n) for n = 1..1000</a>
%H A181809 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a>
%e A181809 The number 12 is both highly composite (A002182(5) = 12) and twice another highly composite number (12 = 2*6 = 2*A002182(4)).  It therefore has more divisors (A002183(5)=6) than any smaller positive integer, and more even divisors (A002183(4)=4) than any smaller positive integer. Since 12 is the third positive integer with the properties that define this sequence, a(3)=12.
%Y A181809 Numbers n such that 1 and 2 both appear in row n of A181803. See also A181808, A181810.
%Y A181809 A053624 gives numbers that set records for number of odd divisors. No number sets records both for its number of odd divisors and its number of even divisors. Only the number 1 sets a record for its number of odd divisors and its number of total divisors.
%Y A181809 Subsequence of A025487.
%K A181809 nonn
%O A181809 1,1
%A A181809 _Matthew Vandermast_, Nov 27 2010