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A086550
Smallest k such that tau(k) - tau(k-1) = n, where tau(k) = number of divisors of k, or 0 if no such number exists.
5
3, 2, 6, 50, 12, 36, 24, 400, 48, 1850, 60, 144, 120, 1600, 168, 576, 180, 1296, 240, 4356, 630, 2304, 360, 900, 960, 9216, 1008, 40000, 720, 20736, 840, 5184, 1800, 46656, 1260, 36864, 1680, 7056, 3024, 986050, 2880, 3600, 6480, 82944, 2520, 193600, 3360
OFFSET
0,1
COMMENTS
Conjecture: No term is zero.
a(2k+1) is either a square or one more than a square. - David Wasserman, Mar 24 2005
LINKS
Giovanni Resta, Table of n, a(n) for n = 0..1000 (first 500 terms from Donovan Johnson)
EXAMPLE
a(3) = 50 as tau(50) - tau(49) = 6 - 3 = 3.
MATHEMATICA
With[{tau=Partition[DivisorSigma[0, Range[10^6]], 2, 1]}, Flatten[ Table[ Position[ #[[2]]-#[[1]]&/@tau, n, 1, 1], {n, 0, 50}]]]+1 (* Harvey P. Dale, Aug 20 2017 *)
PROG
(PARI) /* finds first 100 terms */ nn=vector(100); nd1=1; for(k=2, 24285184, nd2=numdiv(k); d=nd2-nd1; if(d>0, if(d<=100, if(nn[d]==0, nn[d]=k))); nd1=nd2); for(n=1, 100, write("b086550.txt", n " " nn[n])) /* Donovan Johnson, Sep 25 2013 */
CROSSREFS
Cf. A285457.
Sequence in context: A334588 A025240 A137602 * A266239 A018864 A271610
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Aug 28 2003
EXTENSIONS
Corrected and extended by David Wasserman, Mar 24 2005
Offset changed to 0, and a(0) added by Giovanni Resta, Apr 28 2017
STATUS
approved