

A030626


Numbers with 8 divisors.


24



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
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OFFSET

1,1


COMMENTS

a(n)= product of a prime and the cube of another prime or a(n) = product of three distinct primes (squarefree number with three prime factors) or a(n) = p^7 where p is prime.  Amarnath Murthy, Apr 21 2001. Case I: a(n) = p^3*q, a(1)= 24 = 2^3*3, proper divisor product = 13824=24^3. Case II: a(n) = p*q*r a(2) = 30 = 2*3*5, proper divisor product = 27000=30^3. Case III: a(n) = p^7 a(14) = 128 = 2^7, proper divisor product = 2^21. Here p, q, r are distinct primes.
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

R. J. Mathar, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Divisor Product.


FORMULA

A000005(a(n))=8.  JuriStepan Gerasimov, Oct 10 2009
Union A065036 U A007304 U A092759.  R. J. Mathar, Apr 03 2011


MAPLE

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


MATHEMATICA

f[n_]:=Length[Divisors[n]]==8; Select[Range[400], f] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)


PROG

(PARI) Vec(select(x>x==8, vector(500, i, numdiv(i)), 1)) \\ Michel Marcus, Dec 17 2014


CROSSREFS

Essentially the same as A111398.
Sequence in context: A129656 A048945 A111398 * A125639 A076496 A125640
Adjacent sequences: A030623 A030624 A030625 * A030627 A030628 A030629


KEYWORD

nonn


AUTHOR

Jeff Burch


STATUS

approved



