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 A067128 Ramanujan's largely composite numbers, defined to be numbers n such that d(n) >= d(k) for k = 1 to n-1. 31
 1, 2, 3, 4, 6, 8, 10, 12, 18, 20, 24, 30, 36, 48, 60, 72, 84, 90, 96, 108, 120, 168, 180, 240, 336, 360, 420, 480, 504, 540, 600, 630, 660, 672, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 3780, 3960, 4200, 4320, 4620, 4680, 5040, 7560, 9240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is a subset of A034287; are they identical? They match for n up to 1500000. Equals A034287 for the 105834 terms less than 10^150. Every subsequence of terms, having the fixed greatest prime divisor prime(k), k=1,2,..., is finite. For a proof see in A273015. The list of these subsequences begin {2,4,8}, {3,6,12,18,24,36,48,72,96,108}, ... - Vladimir Shevelev, May 13 2016 By a result of Erdős (1944), a(n + 1) <= 2 * a(n): see Erdős. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 P. Erdős, On Highly composite numbers, J. London Math. Soc. 19 (1944), 130--133 MR7,145d; Zentralblatt 61,79. Jean-Louis Nicolas, Répartition des nombres largement composés, Acta Arithmetica 34 (1979), 379-390. J.-L. Nicolas and G. Robin, Highly Composite Numbers by Srinivasa Ramanujan, The Ramanujan Journal, Vol. 1(2), pp. 119-153, Kluwer Academics Pub. Vladimir Shevelev, On Erdős constant, arXiv:1605.08884 [math.NT], 2016. EXAMPLE 8 is a term as d(8) = 4 and d(k) <= 4 for k = 1,...,7. MATHEMATICA For[n=1; max=0, True, n++, If[(d=DivisorSigma[0, n])>=max, Print[n]; max=d]] PROG (PARI) is(n) = my(nd=numdiv(n)); for(k=1, n-1, if(numdiv(k) > nd, return(0))); return(1) \\ Felix Fröhlich, May 22 2016 CROSSREFS For n with strictly increasing number of divisors, see A002182; A272314, A273011 (infinitary analog), subsequences A273015, A273016, A273018. Number of divisors of a(n): A273353. Sequence in context: A074715 A216365 A034287 * A245779 A120432 A020490 Adjacent sequences:  A067125 A067126 A067127 * A067129 A067130 A067131 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Jan 09 2002 EXTENSIONS Edited by Dean Hickerson, Jan 15 2002 and by T. D. Noe, Nov 07 2002 STATUS approved

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Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)