login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (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.

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. - 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

AUTHOR

Jeff Burch

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 7 05:39 EST 2016. Contains 278841 sequences.