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A181794 Numbers n such that the number of even divisors of n is an even divisor of n.

%I A181794 #19 Aug 29 2019 05:05:56
%S A181794 4,6,10,12,14,16,20,22,24,26,28,34,36,38,44,46,48,52,58,62,68,74,76,
%T A181794 80,82,86,90,92,94,106,112,116,118,120,122,124,126,134,142,144,146,
%U A181794 148,150,158,160,164,166,168,172,176,178,180,188,192,194,198,202,206,208,212,214,216,218,226,234,236,240,244,252,254,256,262,264,268,272,274,278
%N A181794 Numbers n such that the number of even divisors of n is an even divisor of n.
%C A181794 All terms are even, since odd numbers, even if they have an even count of divisors, don't have any even divisors.
%C A181794 Includes all numbers of the form A000040(m)*A001146(n).
%H A181794 Amiram Eldar, <a href="/A181794/b181794.txt">Table of n, a(n) for n = 1..10000</a>
%e A181794 a(4)=12 has four even divisors (2, 4, 6, and 12), and 4 is one of those even divisors.
%e A181794 The number 21 is not in this sequence: it has four divisors (1, 3, 7, and 21), and 4 is not one of those divisors.
%t A181794 Select[Range[2, 1000, 2], EvenQ[DivisorSigma[0, #/2]] && MemberQ[Divisors[#], DivisorSigma[0, #/2]] &]
%t A181794 Select[Range[2, 278, 2], EvenQ[(d = DivisorSigma[0, #/2])] && Divisible[#, d] &] (* _Amiram Eldar_, Aug 29 2019 *)
%Y A181794 A100484 and A001749 are subsequences. A001146 and A100042 are also subsequences except for their initial terms.
%Y A181794 See also A033950, A049439, A181795.
%K A181794 nonn
%O A181794 1,1
%A A181794 _Matthew Vandermast_, Nov 14 2010
%E A181794 Verified and edited by _Alonso del Arte_, Nov 17 2010