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%I #39 Sep 08 2022 08:46:03
%S 3,5,8,11,23,28,29,40,41,53,83,89,92,113,124,131,164,173,175,179,188,
%T 191,192,220,233,236,239,244,251,268,281,293,316,325,356,359,419,431,
%U 443,448,452,491,507,509,593,628,641,653,659,668,683,692,719,743,747,761,764
%N Numbers n such that tau(4n+2)=tau(4n)-2, where tau=A000005 gives the number of divisors.
%C Motivated by the observation from A. Wesolowski that Sophie Germain primes A005384 satisfy this relation. A005384 is indeed exactly the subsequence of all primes in this sequence.
%C If p is an odd prime and 8*p+1 is in A006881, then 4*p is in the sequence. - _Robert Israel_, May 11 2016
%H Robert Israel, <a href="/A215751/b215751.txt">Table of n, a(n) for n = 1..10000</a>
%p filter:= n -> numtheory:-tau(4*n+2)=numtheory:-tau(4*n)-2:
%p select(filter, [$1..1000]); # _Robert Israel_, May 11 2016
%t Select[Range@ 800, DivisorSigma[0, 4 # + 2] == DivisorSigma[0, 4 #] - 2 &] (* _Michael De Vlieger_, May 12 2016 *)
%o (PARI) for(n=1,999,numdiv(4*n+2)==numdiv(4*n)-2 & print1(n","))
%o (Magma) [n: n in [1..764] | NumberOfDivisors(4*n+2) eq NumberOfDivisors(4*n)-2]; // _Arkadiusz Wesolowski_, May 11 2016
%Y Cf. A005384, A006881.
%K nonn
%O 1,1
%A _M. F. Hasler_, Aug 25 2012