

A001747


2 together with primes multiplied by 2.


37



2, 4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502
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OFFSET

1,1


COMMENTS

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
Sequence gives solutions of sigma(n)  phi(n) = n + tau(n) where tau(n) is the number of divisors of n.
Numbers n such that sigma(n) = 3*(n  phi(n)).
Except for 2, orders of noncyclic groups k (in A060679(n)) such that x^k==1 (mod k) has only 1 solution 2<=x<=k.  Benoit Cloitre, May 10 2002
Numbers n such that A092673(n) = 2.  Jon Perry, Mar 02 2004
Except for initial terms, this sequence = A073582 = A074845 = A077017. Starting with the term 10, they are identical.  Robert G. Wilson v, Jun 15 2004
Together with 8 and 16, even numbers n such that n^2 does not divide (n/2)!.  Arkadiusz Wesolowski, Jul 16 2011
Twice noncomposite numbers.  Omar E. Pol, Jan 30 2012


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A001043(n)  A001223(n+1), except for initial term.
a(n) = A116366(n2,n2) for n>2.  Reinhard Zumkeller, Feb 06 2006
A006093(n) = A143201(a(n+1)) for n>1.  Reinhard Zumkeller, Aug 12 2008
a(n) = 2*A008578(n).  Omar E. Pol, Jan 30 2012, and Reinhard Zumkeller, Feb 16 2012


MATHEMATICA

Join[{2}, 2*Prime[Range[60]]] (* Harvey P. Dale, Jul 23 2013 *)


PROG

(PARI) print1(2); forprime(p=2, 97, print1(", "2*p)) \\ Charles R Greathouse IV, Jan 31 2012
(MAGMA) [2] cat [2*NthPrime(n): n in [1..60]]; // G. C. Greubel, May 18 2019
(Sage) [2]+[2*nth_prime(n) for n in (1..60)] # G. C. Greubel, May 18 2019
(GAP) Concatenation([2], List([1..60], n> 2*Primes[n])) # G. C. Greubel, May 18 2019


CROSSREFS

Cf. A060679, A009530, A098764.
Equals {2} UNION {A100484}.
Sequence in context: A237758 A023499 A103445 * A048670 A333315 A307889
Adjacent sequences: A001744 A001745 A001746 * A001748 A001749 A001750


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



