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
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
(Python)
from math import prod
from itertools import count
from sympy import factorint
def A055234(n):
for m in count(1):
f = factorint(m)
if n*m*prod((p-1)**2 for p in f)==prod(p**(e+2)-p for p, e in f.items()):
return m # Chai Wah Wu, Aug 12 2024
CROSSREFS
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