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 A002473 7-smooth numbers: positive numbers whose prime divisors are all <= 7. (Formerly M0477 N0177) 102
 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 humble numbers; sometimes also called highly composite numbers, but this usually refers to A002182. Successive numbers k such that phi(210k) = 48k. - Artur Jasinski, Nov 05 2008 The divisors of 10! (A161466) are a finite subsequence. - Reinhard Zumkeller, Jun 10 2009 Numbers n such that A198487(n) > 0 and A107698(n) > 0. - Jaroslav Krizek, Nov 04 2011 A262401(a(n)) = a(n). - Reinhard Zumkeller, Sep 25 2015 Numbers which are products of single-digit numbers. - N. J. A. Sloane, Jul 02 2017 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 R. Zumkeller, Table of n, a(n) for n = 1..10000 (first 5841 terms from N. J. A. Sloane) Raphael Schumacher, The Formulas for the Distribution of the 3-Smooth, 5-Smooth, 7-Smooth and all other Smooth Numbers, arXiv preprint arXiv:1608.06928 [math.NT], 2016. 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 (* 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", "))) (PARI) is_A002473(n)=n<11||vecmax(factor(n, 7)[, 1])<8 \\ M. F. Hasler, Jan 16 2015 (PARI) list(lim)=my(v=List(), t); for(a=0, logint(lim\1, 7), for(b=0, logint(lim\7^a, 5), for(c=0, logint(lim\7^a\5^b, 3), t=3^c*5^b*7^a; while(t<=lim, listput(v, t); t<<=1)))); Set(v) \\ Charles R Greathouse IV, Feb 22 2017 (Haskell) import Data.Set (singleton, deleteFindMin, fromList, union) 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 Subsequence of A080672, complement of A068191. Subsequences: A003591, A003594, A003595, A195238, A059405. Not the same as A063938. For p-smooth numbers with other values of p, see A003586, A051037, A051038, A080197, A080681, A080682, A080683. Cf. A002182, A067374, A210679, A238985 (zeroless terms), A006530. Cf. A262401. Sequence in context: A225737 A079333 A063938 * A174995 A161466 A178863 Adjacent sequences:  A002470 A002471 A002472 * A002474 A002475 A002476 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 23 1999 Additional comments from Michel Lecomte, Jun 09 2007 Edited by M. F. Hasler, Jan 16 2015 STATUS approved

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