The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005279 Numbers having divisors d,e with d < e < 2*d. (Formerly M4093) 30
 6, 12, 15, 18, 20, 24, 28, 30, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 66, 70, 72, 75, 77, 78, 80, 84, 88, 90, 91, 96, 99, 100, 102, 104, 105, 108, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 140, 143, 144, 150, 153, 154, 156, 160, 162, 165, 168, 170, 174, 175, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The arithmetic and harmonic means of A046793(n) and a(n) are both integers. n is in this sequence iff n is a multiple of some term in A020886. a(n) is also a positive integer v for which there exists a smaller positive integer u such that the contraharmonic mean (uu+vv)/(u+v) is an integer c (in fact, there are two distinct values u giving with v the same c). - Pahikkala Jussi, Dec 14 2008 A174903(a(n)) > 0; complement of A174905. - Reinhard Zumkeller, Apr 01 2010 Also numbers n such that A239657(n) > 0. - Omar E. Pol, Mar 23 2014 Erdős (1948) shows that this sequence has a natural density, so a(n) ~ k*n for some constant k. It can be shown that k < 3.03, and by numerical experiments it seems that k is around 1.8. - Charles R Greathouse IV, Apr 22 2015 Numbers k such that at least one of the parts in the symmetric representation of sigma(k) has width > 1. - Omar E. Pol, Dec 08 2016 Erdős conjectured that the asymptotic density of this sequence is 1. The numbers of terms not exceeding 10^k for k = 1, 2, ... are 1, 32, 392, 4312, 45738, 476153, 4911730, 50359766, 513682915, 5224035310, ... - Amiram Eldar, Jul 21 2020 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, E3. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000, first 1000 terms from T. D. Noe Paul Erdős, On the density of some sequences of numbers, Bull. Amer. Math. Soc. 54 (1948), 685--692 MR10,105b; Zbl 32,13 (see Theorem 3). Paul Erdős, Some unconventional problems in number theory, Journées Arithmétiques de Luminy, Astérisque 61 (1979), p. 73-82. Paul Erdős, Some unconventional problems in number theory, Mathematics Magazine, Vol. 52, No. 2 (1979), pp. 67-70. Paul Erdős, On some applications of probability to analysis and number theory, J. London Math. Soc., Vol. 39, No. 1 (1964), pp. 692-696, alternative link. Planet Math., Integer Contraharmonic Means, Proposition 4. Planet Math., Contraharmonic proportion Robert G. Wilson v, Letter, N.D. FORMULA a(n) = A010814(n)/2. - Omar E. Pol, Dec 04 2016 MAPLE isA005279 := proc(n) local divs, d, e ; divs := numtheory[divisors](n) ; for d from 1 to nops(divs)-1 do for e from d+1 to nops(divs) do if divs[e] < 2*divs[d] then RETURN(true) ; fi ; od: od: RETURN(false) : end; for n from 3 to 300 do if isA005279(n) then printf("%d, ", n) ; fi ; od : # R. J. Mathar, Jun 08 2006 MATHEMATICA aQ[n_] := Select[Partition[Divisors[n], 2, 1], #[] < 2 #[] &] != {}; Select[Range, aQ] (* Jayanta Basu, Jun 28 2013 *) PROG (Haskell) a005279 n = a005279_list !! (n-1) a005279_list = filter ((> 0) . a174903) [1..] -- Reinhard Zumkeller, Sep 29 2014 (PARI) is(n)=my(d=divisors(n)); for(i=3, #d, if(d[i]<2*d[i-1], return(1))); 0 \\ Charles R Greathouse IV, Apr 22 2015 CROSSREFS Cf. A010814, A089341, A020886, A046793, A174903, A174905, A237271, A237593, A239657. Sequence in context: A219095 A107487 A092671 * A343281 A129512 A259366 Adjacent sequences:  A005276 A005277 A005278 * A005280 A005281 A005282 KEYWORD nonn AUTHOR 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)