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A007416 The minimal numbers: sequence A005179 arranged in increasing order.
(Formerly M1022)
36
1, 2, 4, 6, 12, 16, 24, 36, 48, 60, 64, 120, 144, 180, 192, 240, 360, 576, 720, 840, 900, 960, 1024, 1260, 1296, 1680, 2520, 2880, 3072, 3600, 4096, 5040, 5184, 6300, 6480, 6720, 7560, 9216, 10080, 12288, 14400, 15120, 15360, 20160, 25200, 25920, 27720, 32400, 36864, 44100 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers k such that there is no x < k such that A000005(x) = A000005(k). - Benoit Cloitre, Apr 28 2002

Brown notes that A002182 is a subsequence. - Charles R Greathouse IV, Jun 07 2013

A047983(a(n)) = 0. - Reinhard Zumkeller, Nov 03 2015

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

REFERENCES

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

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

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Ron Brown, The minimal number with a given number of divisors (2009), Journal of Number Theory 116:1 (2005), pp. 150-158.

M. E. Grost, The smallest number with a given number of divisors, Amer. Math. Monthly, 75 (1968), 725-729.

J. Roberts, Lure of the Integers, Annotated scanned copy of pp. 81, 86 with notes.

Anna K. Savvopoulou and Christopher M. Wedrychowicz, On the smallest number with a given number of divisors, The Ramanujan Journal, 2015, Vol. 37, pp. 51-64.

MAPLE

for n from 1 to 10^5 do

  t:= numtheory:-tau(n);

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

od:

sort(map(op, [entries(B)])); # Robert Israel, Nov 11 2015

MATHEMATICA

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 *)

PROG

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

(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

(Haskell)

a007416 n = a007416_list !! (n-1)

a007416_list = f 1 [] where

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

            where tau = a000005' x

-- Reinhard Zumkeller, Apr 18 2015

CROSSREFS

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

Cf. A000005, A002182, A047983.

Sequence in context: A089696 A171609 A099316 * A293132 A098895 A266543

Adjacent sequences:  A007413 A007414 A007415 * A007417 A007418 A007419

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 26 20:18 EST 2020. Contains 332295 sequences. (Running on oeis4.)