OFFSET
1,2
COMMENTS
Numbers k such that there is no x < k such that A000005(x) = A000005(k). - Benoit Cloitre, Apr 28 2002
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
Charles R Greathouse IV, Table of n, a(n) for n = 1..100000 (first 1000 from T. D. Noe and to 10000 from David A. Corneth)
Ron Brown, The minimal number with a given number of divisors, 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-François 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
(PARI)
A283980(n, f=factor(n))=prod(i=1, #f~, my(p=f[i, 1]); if(p==2, 6, nextprime(p+1))^f[i, 2])
A025487do(e) = my(v=List([1, 2]), i=2, u = 2^e, t); while(v[i] != u, if(2*v[i] <= u, listput(v, 2*v[i]); t = A283980(v[i]); if(t <= u, listput(v, t))); i++); Set(v)
winnow(v, lim=v[#v])=my(m=Map(), u=List()); for(i=1, #v, if(v[i]>lim, break); my(t=numdiv(v[i])); if(!mapisdefined(m, t), mapput(m, t, 0); listput(u, v[i]))); m=0; Vec(u)
list(lim)=winnow(A025487do(logint(lim\1-1, 2)+1), lim) \\ Charles R Greathouse IV, Nov 17 2022
(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
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved