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A049642 Numbers k such that the number of divisors of k does not divide the sum of divisors of k.

%I A049642 #41 Apr 25 2024 09:12:06
%S A049642 2,4,8,9,10,12,16,18,24,25,26,28,32,34,36,40,48,50,52,58,63,64,72,74,
%T A049642 75,76,80,81,82,84,88,90,98,100,104,106,108,112,117,120,121,122,124,
%U A049642 128,130,136,144,146,148,152,156,160,162,170,171,172,175
%N A049642 Numbers k such that the number of divisors of k does not divide the sum of divisors of k.
%D A049642 József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 119, section III.51.
%H A049642 Reinhard Zumkeller, <a href="/A049642/b049642.txt">Table of n, a(n) for n = 1..10000</a>
%H A049642 Wikipedia, <a href="http://en.wikipedia.org/wiki/Arithmetic_number">Arithmetic number</a>.
%F A049642 A054025(a(n)) > 0. - _Reinhard Zumkeller_, Jan 06 2012
%F A049642 A245656(a(n)) = 0. - _Reinhard Zumkeller_, Jul 28 2014
%p A049642 isA049642 := proc(n)
%p A049642     if modp(numtheory[sigma](n),numtheory[tau](n)) = 0 then
%p A049642         false;
%p A049642     else
%p A049642         true;
%p A049642     end if;
%p A049642 end proc:
%p A049642 A049642 := proc(n)
%p A049642     option remember;
%p A049642     if n = 1 then
%p A049642         2;
%p A049642     else
%p A049642         for a from procname(n-1)+1 do
%p A049642             if isA049642(a) then
%p A049642                 return a;
%p A049642             end if;
%p A049642         end do:
%p A049642     end if;
%p A049642 end proc: # _R. J. Mathar_, Oct 26 2015
%t A049642 Select[Range[175], Mod[DivisorSigma[1, #], DivisorSigma[0, #]] > 0 &] (* _Jayanta Basu_, Mar 28 2013 *)
%o A049642 (Haskell)
%o A049642 a049642 n = a049642_list !! (n-1)
%o A049642 a049642_list = filter ((== 0) . a245656) [1..]
%o A049642 -- _Reinhard Zumkeller_, Jan 06 2012
%o A049642 (GAP) a:=Filtered([1..180],n->Sigma(n) mod Tau(n)>0);; Print(a); # _Muniru A Asiru_, Jan 25 2019
%o A049642 (PARI) is(n) = {my(f = factor(n)); sigma(f) % numdiv(f) > 0;} \\ _Amiram Eldar_, Apr 25 2024
%Y A049642 Complement of A003601.
%Y A049642 Cf. A000005, A000203.
%Y A049642 Cf. A054025, A245656.
%K A049642 nonn,easy
%O A049642 1,1
%A A049642 _N. J. A. Sloane_