%I #48 Sep 08 2022 08:44:29

%S 2,4,6,10,14,22,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,

%T 158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,

%U 334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502

%N 2 together with primes multiplied by 2.

%C When supplemented with 8, may be considered the "even primes", since these are the even numbers n = 2k which are divisible just by 1, 2, k and 2k. - Louis Zuckerman (louis(AT)trapezoid.com), Sep 12 2000

%C Sequence gives solutions of sigma(n) - phi(n) = n + tau(n) where tau(n) is the number of divisors of n.

%C Numbers n such that sigma(n) = 3*(n - phi(n)).

%C Except for 2, orders of non-cyclic groups k (in A060679(n)) such that x^k==1 (mod k) has only 1 solution 2<=x<=k. - _Benoit Cloitre_, May 10 2002

%C Numbers n such that A092673(n) = 2. - _Jon Perry_, Mar 02 2004

%C Except for initial terms, this sequence = A073582 = A074845 = A077017. Starting with the term 10, they are identical. - _Robert G. Wilson v_, Jun 15 2004

%C Together with 8 and 16, even numbers n such that n^2 does not divide (n/2)!. - _Arkadiusz Wesolowski_, Jul 16 2011

%C Twice noncomposite numbers. - _Omar E. Pol_, Jan 30 2012

%H T. D. Noe, <a href="/A001747/b001747.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A001043(n) - A001223(n+1), except for initial term.

%F a(n) = A116366(n-2,n-2) for n>2. - _Reinhard Zumkeller_, Feb 06 2006

%F A006093(n) = A143201(a(n+1)) for n>1. - _Reinhard Zumkeller_, Aug 12 2008

%F a(n) = 2*A008578(n). - _Omar E. Pol_, Jan 30 2012, and _Reinhard Zumkeller_, Feb 16 2012

%t Join[{2},2*Prime[Range[60]]] (* _Harvey P. Dale_, Jul 23 2013 *)

%o (PARI) print1(2);forprime(p=2,97,print1(", "2*p)) \\ _Charles R Greathouse IV_, Jan 31 2012

%o (Magma) [2] cat [2*NthPrime(n): n in [1..60]]; // _G. C. Greubel_, May 18 2019

%o (Sage) [2]+[2*nth_prime(n) for n in (1..60)] # _G. C. Greubel_, May 18 2019

%o (GAP) Concatenation([2], List([1..60], n-> 2*Primes[n])) # _G. C. Greubel_, May 18 2019

%Y Cf. A060679, A009530, A098764.

%Y Equals {2} UNION {A100484}.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_