A030626 Numbers with exactly 8 divisors.

24, 30, 40, 42, 54, 56, 66, 70, 78, 88, 102, 104, 105, 110, 114, 128, 130, 135, 136, 138, 152, 154, 165, 170, 174, 182, 184, 186, 189, 190, 195, 222, 230, 231, 232, 238, 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

Offset

1,1

Comments

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

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from R. J. Mathar)

Jérôme Germoni, Nombres à huit diviseurs, Images des Mathématiques, CNRS, 2017 (in French).

Eric Weisstein's World of Mathematics, Divisor Product.

Formula

A000005(a(n))=8. - Juri-Stepan Gerasimov, Oct 10 2009

Equals A065036 (p*q^3) U A007304 (p*q*r) U A092759 (p^7). - Amarnath Murthy, Apr 21 2001

Maple

select(numtheory:-tau=8, [$1..1000]); # Robert Israel, Dec 17 2014

Mathematica

Select[Range[400], DivisorSigma[0, #]== 8 &] (* Vincenzo Librandi, Oct 05 2017 *)

Prog

(PARI) Vec(select(x->x==8, vector(500, i, numdiv(i)), 1)) \\ Michel Marcus, Dec 17 2014
(Magma) [n: n in [1..400] | DivisorSigma(0, n) eq 8]; // Vincenzo Librandi, Oct 05 2017
(Python)
from sympy import divisor_count
isok = lambda n: divisor_count(n) == 8
print([n for n in range(1, 400) if isok(n)]) # Darío Clavijo, Oct 17 2023

Crossrefs

Essentially the same as A111398.

Cf. A000005, A007304, A049053, A065036, A092759, A119479.

Sequence in context: A334974 A048945 A111398 * A302571 A335054 A379872

Adjacent sequences: A030623 A030624 A030625 * A030627 A030628 A030629

Keyword

nonn,changed

Author

Jeff Burch

Status

approved