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A007416 The minimal numbers: sequence A005179 arranged in increasing order.
(Formerly M1022)
36

%I M1022

%S 1,2,4,6,12,16,24,36,48,60,64,120,144,180,192,240,360,576,720,840,900,

%T 960,1024,1260,1296,1680,2520,2880,3072,3600,4096,5040,5184,6300,6480,

%U 6720,7560,9216,10080,12288,14400,15120,15360,20160,25200,25920,27720,32400,36864,44100

%N The minimal numbers: sequence A005179 arranged in increasing order.

%C Numbers k such that there is no x < k such that A000005(x) = A000005(k). - _Benoit Cloitre_, Apr 28 2002

%C Brown notes that A002182 is a subsequence. - _Charles R Greathouse IV_, Jun 07 2013

%C A047983(a(n)) = 0. - _Reinhard Zumkeller_, Nov 03 2015

%C Subsequence of A025487. If some m in A025487 is the first term in that sequence having its number of divisors, m is in this sequence. - _David A. Corneth_, Aug 31 2019

%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 86.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H David A. Corneth, <a href="/A007416/b007416.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%H Ron Brown, <a href="https://doi.org/10.1016/j.jnt.2005.04.004">The minimal number with a given number of divisors</a>, Journal of Number Theory 116:1 (2005), pp. 150-158.

%H M. E. Grost, <a href="http://www.jstor.org/stable/2315183">The smallest number with a given number of divisors</a>, Amer. Math. Monthly, 75 (1968), 725-729.

%H J. Roberts, <a href="/A007415/a007415.pdf">Lure of the Integers</a>, Annotated scanned copy of pp. 81, 86 with notes.

%H Anna K. Savvopoulou and Christopher M. Wedrychowicz, <a href="http://dx.doi.org/10.1007/s11139-014-9572-9">On the smallest number with a given number of divisors</a>, The Ramanujan Journal, 2015, Vol. 37, pp. 51-64.

%p for n from 1 to 10^5 do

%p t:= numtheory:-tau(n);

%p if not assigned(B[t]) then B[t]:= n fi;

%p od:

%p sort(map(op,[entries(B)]));# _Robert Israel_, Nov 11 2015

%t A007416 = Reap[ For[ s = 1, s <= 10^5, s++, If[ Abs[ Product[ DivisorSigma[0, i] - DivisorSigma[0, s], {i, 1, s-1}]] > 0, Print[s]; Sow[s]]]][[2, 1]] (* _Jean-Fran├žois Alcover_, Nov 19 2012, after Pari *)

%o (PARI) for(s=1,10^6,if(abs(prod(i=1,s-1,numdiv(i)-numdiv(s)))>0,print1(s,",")))

%o (PARI) is(n)=my(d=numdiv(n));for(i=1,n-1,if(numdiv(i)==d, return(0))); 1 \\ _Charles R Greathouse IV_, Feb 20 2013

%o (Haskell)

%o a007416 n = a007416_list !! (n-1)

%o a007416_list = f 1 [] where

%o f x ts = if tau `elem` ts then f (x + 1) ts else x : f (x + 1) (tau:ts)

%o where tau = a000005' x

%o -- _Reinhard Zumkeller_, Apr 18 2015

%Y Cf. A005179, A025487, A099317, A099312, A099314, A099316, A099318.

%Y Cf. A000005, A002182, A047983.

%K nonn,easy,nice

%O 1,2

%A _N. J. A. Sloane_

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Last modified April 10 11:35 EDT 2021. Contains 342845 sequences. (Running on oeis4.)