1,2

A061987(n)=a(n+1)-a(n), a(A084791(n))=A084789(n), a(A084791(n)+1)=A084790(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 03 2003

Successive numbers k such EulerPhi[6 k] == 2 k. [From Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008]

Where record values greater than 1 occur in A088468: A160519(n)=A088468(a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 16 2009]

R. Blecksmith, M. McCallum and J. L. Selfridge, 3-smooth representations of integers, Amer. Math. Monthly, 105 (1998), 529-543.

J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 654 pp; 85; 287-8, Ellipses Paris 2004.

D. J. Mintz, 2,3 sequence as a binary mixture, Fib. Quarterly, Vol. 19, No 4, Oct 1981, pp. 351-360.

S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, p. xxiv.

R. Tijdeman, Some applications of Diophantine approximation, pp. 261-284 of Surveys in Number Theory (Urbana, May 21, 2000), ed. M. A. Bennett et al., Peters, 2003.

Franklin T. Adams-Watters, Table of n, a(n) for n = 1..501

H. W. Lenstra Jr., Harmonic Numbers

I. Peterson, Medieval Harmony

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

An asymptotic formula for a(n) is roughly : a(n)= 1/sqrt(6)*EXP(sqrt(2*ln(2)*ln(3)*n)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 20 2001

Union of powers of 2 and 3 with n such that psi(n)=2n, where psi(n)=n*Product_(1+1/p) over all prime factors p of n. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 07 2004

Sort[ Flatten[ Table[ 2^i*3^j, {i, 0, 12}, {j, 0, 8} ] ] ]

a[1] = 1; j = 1; k = 1; n = 100; For[k = 2, k <= n, k++, If[2*a[k - j] < 3^j, a[k] = 2*a[k - j], {a[k] = 3^j, j++}]] Table[a[i], {i, 1, n}] (Hai He (hai(AT)mathteach.net) and Gilbert Traub, Dec 28 2004)

aa = {}; Do[If[EulerPhi[6 n] == 2 n, AppendTo[aa, n]], {n, 1, 1000}]; aa [From Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008]

(PARI) test(n)= {m=n; for(p=2, 3, while(m%p==0, m=m/p)); return(m==1)} for(n=1, 4000, if(test(n), print1(n", ")))

For p-smooth numbers with other values of p, see A051037, A002473, A051038, A080197, A080681, A080682, A080683.

a(n) = 2^A022328(n)*3^A022329(n). - N. J. A. Sloane, Mar 19 2009

Cf. A117221, A105420, A062051, A117222, A105420, A117220, A090184.

Cf. A131096, A131097.

A088468, A061987. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 16 2009]

Sequence in context: A053640 A097755 A083854 this_sequence A114334 A018690 A018452

Adjacent sequences: A003583 A003584 A003585 this_sequence A003587 A003588 A003589

nonn,easy,nice

Paul.Zimmermann(AT)loria.fr (Paul Zimmermann)

Deleted claim that this sequence is union of 2^n (A000079) and 3^n (A000244) sequences - this does not include the terms which are not pure powers. - Walter Roscello (wroscello(AT)comcast.net), Nov 16 2008

Corrected formula from Lekraj Beedassy - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Mar 19 2009