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A030626 Numbers with 8 divisors. 22
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 (list; graph; refs; listen; history; text; internal format)
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.

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. - Juri-Stepan 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,changed

AUTHOR

Jeff Burch

STATUS

approved

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Last modified December 20 01:21 EST 2014. Contains 252240 sequences.