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A181794 Numbers n such that the number of even divisors of n is an even divisor of n. 3


%S 4,6,10,12,14,16,20,22,24,26,28,34,36,38,44,46,48,52,58,62,68,74,76,

%T 80,82,86,90,92,94,106,112,116,118,120,122,124,126,134,142,144,146,

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

%C All terms are even, since odd numbers, even if they have an even count of divisors, don't have any even divisors.

%C Includes all numbers of the form A000040(m)*A001146(n).

%H Amiram Eldar, <a href="/A181794/b181794.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4)=12 has four even divisors (2, 4, 6, and 12), and 4 is one of those even divisors.

%e 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 Select[Range[2, 1000, 2], EvenQ[DivisorSigma[0, #/2]] && MemberQ[Divisors[#], DivisorSigma[0, #/2]] &]

%t Select[Range[2, 278, 2], EvenQ[(d = DivisorSigma[0, #/2])] && Divisible[#, d] &] (* _Amiram Eldar_, Aug 29 2019 *)

%Y A100484 and A001749 are subsequences. A001146 and A100042 are also subsequences except for their initial terms.

%Y See also A033950, A049439, A181795.

%K nonn

%O 1,1

%A _Matthew Vandermast_, Nov 14 2010

%E Verified and edited by _Alonso del Arte_, Nov 17 2010

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)