

A067004


Number of numbers <= n with same number of divisors as n.


7



1, 1, 2, 1, 3, 1, 4, 2, 2, 3, 5, 1, 6, 4, 5, 1, 7, 2, 8, 3, 6, 7, 9, 1, 3, 8, 9, 4, 10, 2, 11, 5, 10, 11, 12, 1, 12, 13, 14, 3, 13, 4, 14, 6, 7, 15, 15, 1, 4, 8, 16, 9, 16, 5, 17, 6, 18, 19, 17, 1, 18, 20, 10, 1, 21, 7, 19, 11, 22, 8, 20, 2, 21, 23, 12, 13, 24, 9, 22, 2, 2, 25, 23, 3, 26, 27
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


LINKS

Paul Tek, Table of n, a(n) for n = 1..10000


FORMULA

Ordinal transform of A000005.  Franklin T. AdamsWatters, Aug 28 2006
a(A000040(n)^(p1)) = n if p is prime.  Robert Israel, May 04 2015


EXAMPLE

a(10)=3 since 6,8,10 each have four divisors. a(11)=5 since 2,3,5,7,11 each have two divisors.


MAPLE

N:= 1000: # to get a(1) to a(N)
R:= Vector(N):
for n from 1 to N do
v:= numtheory:tau(n);
R[v]:= R[v]+1;
A[n]:= R[v];
od:
seq(A[n], n=1..N); # Robert Israel, May 04 2015


PROG

(PARI) a(n)=my(d=numdiv(n)); sum(k=1, n, numdiv(k)==d) \\ Charles R Greathouse IV, Sep 02 2015


CROSSREFS

Cf. A000005, A008479, A058933, A067003. Inverse of A000040, A001248, A030513, A030514, A030515, A030516, A030626, A030627,
A030628, A030629, A030630, A030631, A030632, A030633, A030634, A030635, A030636, A030637, A030638 etc.
Cf. also A079788, A138009.
A047983(n) = a(n)1.
Sequence in context: A303758 A161904 A249336 * A117920 A079617 A079616
Adjacent sequences: A067001 A067002 A067003 * A067005 A067006 A067007


KEYWORD

nonn


AUTHOR

Henry Bottomley, Dec 21 2001


STATUS

approved



