A164650 - OEIS

%I #8 Jul 14 2012 11:32:31

%S 679,10127,20273,672203,971261,1133639,1247129,1336231,1646743,

%T 1701089,2369471,2674969,2722499,2989909,3160079,3597659,4545749,

%U 6333503,7127861,9357101,10574629,20070061,52928293,67931137,74731807,79940069,80704813,93444911,128155333

%N Numbers n such that sigma(n)/phi(n) = 49/36.

%C A subsequence of A011257.

%C If 7^{k+1}-1 = d*D such that p = 2*7^{k+1}*(d+1)-1 and q = 2*(7^{k+1}+D)-1 are distinct primes, then n = 7^k*p*q is a term of this sequence.

%C The same theorem holds for sequences of numbers such that sigma/phi=b^2/(b-1)^2 with other primes b (here b=7), cf. A068390, A164646, A164648.

%H Donovan Johnson, <a href="/A164650/b164650.txt">Table of n, a(n) for n = 1..1000</a>

%o (PARI) for( n=1,1e7, sigma(n)==49/36*eulerphi(n) && print1(n","))

%Y Cf. A000010 (=phi), A000203 (=sigma), A068390 (sigma/phi=4), A163667 (sigma/phi=9), A164646-A164649.

%K nonn

%O 1,1

%A _M. F. Hasler_, Aug 22 2009