This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000705 n-th superior highly composite number A002201(n) is product of first n terms of this sequence. (Formerly M0423 N0162) 6
 2, 3, 2, 5, 2, 3, 7, 2, 11, 13, 2, 3, 5, 17, 19, 2, 23, 7, 29, 3, 31, 2, 37, 41, 43, 47, 5, 53, 59, 2, 11, 61, 3, 67, 71, 73, 79, 13, 83, 89, 2, 97, 101, 103, 107, 7, 109, 113, 17, 127, 131, 137, 139, 3, 5, 149, 151, 19, 2, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Mathematica program uses the fact that the ratio of consecutive superior highly composite numbers is a prime, which was proved by Ramanujan. Ramanujan computed the first 50 terms of this sequence. Related sequences are A004490 and A073751, having to do with colossally abundant numbers. REFERENCES S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962, p. 115. S. Ramanujan, Ramanujan's Papers, pp. 147-9, Ed. B. J. Venkatachala et al., Prism Books, Bangalore 2000. 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 T. D. Noe, Table of n, a(n) for n=1..10000 J. C. Lagarias, An elementary problem equivalent to the Riemann hypothesis, Am. Math. Monthly 109 (#6, 2002), 534-543. Eric Weisstein's World of Mathematics, Superior Highly Composite Number MATHEMATICA pFactor[f_List] := Module[{p = f[[1]], k = f[[2]]}, N[Log[(k + 2)/(k + 1)]/Log[p]]]; maxN = 100; f = {{2, 1}, {3, 0}}; primes = 1; lst = {2}; x = Table[pFactor[f[[i]]], {i, primes + 1}]; For[n = 2, n <= maxN, n++, i = Position[x, Max[x]][[1, 1]]; AppendTo[lst, f[[i, 1]]]; f[[i, 2]]++; If[i > primes, primes++; AppendTo[f, {Prime[i + 1], 0}]; AppendTo[x, pFactor[f[[ -1]]]]]; x[[i]] = pFactor[f[[i]]]]; lst (* T. D. Noe, Nov 01 2002 *) CROSSREFS Cf. A004490, A073751. Sequence in context: A086418 A100761 A027748 * A073751 A319431 A258581 Adjacent sequences:  A000702 A000703 A000704 * A000706 A000707 A000708 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS Edited by T. D. Noe, Nov 01 2002 STATUS approved

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

Last modified November 19 17:17 EST 2018. Contains 317357 sequences. (Running on oeis4.)