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 A055234 Smallest x such that sigma(x) = n*phi(x), or -1 if no such x exists. 12
 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 (list; graph; refs; listen; history; text; internal format)
 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 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 A204990 A086485 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

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)