A055234 Smallest x such that sigma(x) = n*phi(x), or -1 if no such x exists.

1, 3, 2, 14, 56, 6, 12, 42, 30, 168, 2580, 210, 630, 420, 840, 20790, 416640, 9240, 291060, 83160, 120120, 5165160, 1719277560, 43825320, 26860680, 277560360, 1304863560, 569729160, 587133466920, 16522145640, 33044291280, 563462139240, 1140028049160, 9015394227840, 1255683068640, 65361608151840

Offset

1,2

Comments

Conjecture: For each n, a(n) > 0. - Farideh Firoozbakht, Sep 12 2004

a(33) > 10^12. - Donovan Johnson, Mar 06 2012

a(34) <= 9015394227840, a(35) <= 1255683068640. - Giovanni Resta, May 08 2017

Terms after a(36) are > 10^14. a(37) <= 4771397395084320, a(38) <= 2418379501618080, a(39) <= 413956851628320, a(40) <= 1241870554884960, and a(42) <= 50916692750283360. - Jud McCranie, Sep 13 2017

a(38) = 299761858075680, a(39) = 413956851628320. a(37), a(40), and higher terms are > 4.2*10^14. - Jud McCranie, Nov 27 2017

a(37), a(40), and higher terms are > 6.0 x 10^14. - Jud McCranie, Dec 27 2017

Links

Table of n, a(n) for n=1..36.

Formula

a(n) = Min{x : A000203(x)/A000010(x) = n} = Min{x : A023897(x) = n}

Example

sigma(14) = 24 = 4*phi(14), so a(4) = 14.
n = 21: a(21) = 120120 = 2*2*2*3*5*7*11*13, sigma(120120) = 483840 = n*phi(120120), phi(120120) = 23040.

Mathematica

a[n_]:=(For[m=1, DivisorSigma[1, m]!=n EulerPhi[m], m++ ]; m); Do[Print[a[n]], {n, 31}] (* Farideh Firoozbakht, Oct 31 2008 *)

Prog

(PARI) a(n) = {k = 1; while(sigma(k) != n*eulerphi(k), k++); k; } \\ Michel Marcus, Sep 01 2014

Crossrefs

Cf. A000010, A000203, A020492, A023897, A088830.

Sequence in context: A163355 A214885 A145747 * A291051 A342640 A204990

Adjacent sequences: A055231 A055232 A055233 * A055235 A055236 A055237

Keyword

nonn

Author

Jud McCranie, Jun 21 2000

Extensions

More terms from Farideh Firoozbakht, Sep 12 2004

a(32) from Donovan Johnson, Mar 06 2012

a(33) from Giovanni Resta, May 08 2017

a(34)-a(36) from Jud McCranie, Sep 10 2017

Status

approved