|
| |
|
|
A002473
|
|
Highly composite numbers (2): numbers whose prime divisors are all <= 7.
(Formerly M0477 N0177)
|
|
83
|
|
|
|
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, Table of n, a(n) for n=1..5841 [All terms <2*10^9.]
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 = filter ((<= 7) . a006530) [1..]
-- Reinhard Zumkeller, 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.
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
|
| |
|
|
