A135470 - OEIS

%I #17 May 11 2020 13:49:32

%S 18,70,88,132,780,11096,17816,518656,1713592,9928792,11547352,

%T 13499120,17999992,89283592,134094848,173482552,175519344,318836720,

%U 903230984,1081850752,2146926592,16709332608,18543186000,34177937500

%N Composite numbers n that divide 2 * sigma(n) - d(n) [that is, 2 * sum of divisors - number of divisors].

%C It is conjectured that there are no odd terms and that the sequence is infinite.

%C a(25) > 10^12. - _Donovan Johnson_, Nov 15 2013

%H Yong-Gao Chen and Jin-Hui Fang, <a href="http://www.emis.de/journals/INTEGERS/papers/i7/i7.Abstract.html">On n phi(n)d(n) + 2 and n phi(n) sigma(n)+1</a>, INTEGERS: Electronic J. Combinatorial Number Theory: 8 (2008), #A7.

%H Donovan Johnson, <a href="/A135470/a135470.txt">10 terms > 10^12</a>

%t Select[Range[172*10^4],CompositeQ[#]&&Divisible[2*DivisorSigma[1,#]-DivisorSigma[ 0,#],#]&] (* The program generates the first 9 terms of the sequence. To generate more, increase the Range constant. *) (* _Harvey P. Dale_, May 11 2020 *)

%o (PARI) isok(n) = (! isprime(n) && (2*sigma(n) - numdiv(n)) % n == 0) \\ _Michel Marcus_, Jun 09 2013

%K nonn

%O 1,1

%A _R. K. Guy_, Feb 08 2008

%E Corrected by _Emeric Deutsch_, Feb 29 2008

%E a(15)-a(24) from _Donovan Johnson_, Oct 13 2008