%I #74 Oct 19 2024 15:57:32
%S 24,30,40,42,54,56,66,70,78,88,102,104,105,110,114,128,130,135,136,
%T 138,152,154,165,170,174,182,184,186,189,190,195,222,230,231,232,238,
%U 246,248,250,255,258,266,273,282,285,286,290,296,297,310,318,322,328,344,345,351,354,357,366,370,374,375,376,385,399,402
%N Numbers with exactly 8 divisors.
%C Since A119479(8)=7, there are never more than 7 consecutive terms. Runs of 7 consecutive terms start at 171897, 180969, 647385, ... (subsequence of A049053). - _Ivan Neretin_, Feb 08 2016
%H Jon E. Schoenfield, <a href="/A030626/b030626.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from R. J. Mathar)
%H Jérôme Germoni, <a href="http://images-archive.math.cnrs.fr/Nombres-a-huit-diviseurs.html">Nombres à huit diviseurs</a>, Images des Mathématiques, CNRS, 2017 (in French).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorProduct.html">Divisor Product</a>.
%F A000005(a(n))=8. - _Juri-Stepan Gerasimov_, Oct 10 2009
%F Equals A065036 (p*q^3) U A007304 (p*q*r) U A092759 (p^7). - _Amarnath Murthy_, Apr 21 2001
%p select(numtheory:-tau=8, [$1..1000]); # _Robert Israel_, Dec 17 2014
%t Select[Range[400], DivisorSigma[0, #]== 8 &] (* _Vincenzo Librandi_, Oct 05 2017 *)
%o (PARI) Vec(select(x->x==8,vector(500, i, numdiv(i)),1)) \\ _Michel Marcus_, Dec 17 2014
%o (Magma) [n: n in [1..400] | DivisorSigma(0, n) eq 8]; // _Vincenzo Librandi_, Oct 05 2017
%o (Python)
%o from sympy import divisor_count
%o isok = lambda n: divisor_count(n) == 8
%o print([n for n in range(1, 400) if isok(n)]) # _Darío Clavijo_, Oct 17 2023
%Y Essentially the same as A111398.
%Y Cf. A000005, A007304, A049053, A065036, A092759, A119479.
%K nonn
%O 1,1
%A _Jeff Burch_