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

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002473 Highly composite numbers (2): numbers whose prime divisors are all <= 7.
(Formerly M0477 N0177)
90
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 147, 150, 160, 162, 168, 175, 180, 189, 192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also called 7-smooth numbers or humble numbers.

Successive numbers k such EulerPhi[210 k] = 48 k. [From Artur Jasinski, Nov 05 2008]

The divisors of 10! (cf. A161466) are a finite subsequence. [From Reinhard Zumkeller, Jun 10 2009]

Numbers n such that A198487(n) > 0 and A107698(n) > 0. - Jaroslav Krizek, Nov 04 2011

REFERENCES

B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 52.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

N. J. A. Sloane and R. Zumkeller, Table of n, a(n) for n = 1..10000 First 5841 terms by N. J. A. Sloane

University of Ulm, The first 5842 terms

Eric Weisstein's World of Mathematics, Smooth Number

FORMULA

A006530(a(n)) <= 7. [Reinhard Zumkeller, Apr 01 2012]

MATHEMATICA

Select[Range[250], Max[Transpose[FactorInteger[ # ]][[1]]]<=7&]

aa = {}; Do[If[EulerPhi[210 n] == 48 n, AppendTo[aa, n]], {n, 1, 1200}]; aa [From Artur Jasinski, Nov 05 2008]

mxExp = 8; Select[Union[Times @@@ Flatten[Table[Tuples[{2, 3, 5, 7}, n], {n, mxExp}], 1]], # <= 2^mxExp &] (* Harvey P. Dale, Aug 13 2012 *)

mx = 200; Sort@ Flatten@ Table[ 2^i*3^j*5^k*7^l, {i, 0, Log[2, mx]}, {j, 0, Log[3, mx/2^i]}, {k, 0, Log[5, mx/(2^i*3^j)]}, {l, 0, Log[7, mx/(2^i*3^j*5^k)]}] (* Robert G. Wilson v, Aug 17 2012 *)

PROG

(PARI) test(n)= {m=n; forprime(p=2, 7, while(m%p==0, m=m/p)); return(m==1)} for(n=1, 200, if(test(n), print1(n", ")))

(Haskell)

a002473 n = a002473_list !! (n-1)

a002473_list = f $ singleton 1 where

   f s = x : f (s' `union` fromList (map (* x) [2, 3, 5, 7]))

         where (x, s') = deleteFindMin s

-- Reinhard Zumkeller, Mar 08 2014, Apr 02 2012, Apr 01 2012

(MAGMA) [n: n in [1..200] | PrimeDivisors(n) subset PrimesUpTo(7)]; // Bruno Berselli, Sep 24 2012

CROSSREFS

Cf. A002182, A067374. Complement of A068191. Not the same as A063938. For p-smooth numbers with other values of p, see A003586, A051037, A051038, A080197, A080681, A080682, A080683.

Cf. A195238 (subsequence).

Subsequence of A080672, cf. A210679.

Cf. A238985 (zeroless terms).

Sequence in context: A225737 A079333 A063938 * A174995 A161466 A178863

Adjacent sequences:  A002470 A002471 A002472 * A002474 A002475 A002476

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from James A. Sellers, Dec 23 1999

Additional comments from Michel Lecomte, Jun 09 2007

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified April 23 14:29 EDT 2014. Contains 240931 sequences.