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A002473
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Highly composite numbers (2): numbers whose prime divisors are all <= 7.
(Formerly M0477 N0177)
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77
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also called 7-smooth numbers or humble numbers.
Successive numbers k such EulerPhi[210 k] = 48 k. [From Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008]
The divisors of 10! (cf. A161466) are a finite subsequence. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2009]
Numbers n such that A198487(n) > 0 and A107698(n) > 0. - Jaroslav Krizek, Nov 04 2011
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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).
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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, Link to a section of The World of Mathematics.
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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 (grafix(AT)csl.pl), Nov 05 2008]
nn = 1000; Sort[Reap[Do[n = 2^i*3^j*5^k*7^l; If[n <= nn, Sow[n]], {i, 0, Log[2, nn]}, {j, 0, Log[3, nn]}, {k, 0, Log[5, nn]}, {l, 0, Log[7, nn]}]][[2, 1]]] (* T. D. Noe, Mar 07 2011 *)
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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", ")))
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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).
Sequence in context: A056757 A079333 A063938 * A174995 A161466 A178863
Adjacent sequences: A002470 A002471 A002472 * A002474 A002475 A002476
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
Additional comments from Michel Lecomte, Jun 09 2007
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