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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. Adams-Watters, Aug 28 2006

a(A000040(n)^(p-1)) = 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

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Last modified January 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)