A001747 2 together with primes multiplied by 2.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

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 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

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

Crossrefs

Cf. A060679, A009530, A098764.

Equals {2} UNION {A100484}.

Programs

GAP

Concatenation([2], List([1..60], n-> 2*Primes[n])); # G. C. Greubel, May 18 2019

Magma

[2] cat [2*NthPrime(n): n in [1..60]]; // G. C. Greubel, May 18 2019

Mathematica

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

PARI

print1(2);forprime(p=2,97,print1(", "2*p)) \\ Charles R Greathouse IV, Jan 31 2012

Sage

[2]+[2*nth_prime(n) for n in (1..60)] # G. C. Greubel, May 18 2019

Formula

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

a(n) = A116366(n-2,n-2) 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