A067004 Number of numbers <= n with same number of divisors as n.
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
Offset: 1
Keywords
Examples
a(10)=3 since 6,8,10 each have four divisors. a(11)=5 since 2,3,5,7,11 each have two divisors.
Links
- Paul Tek, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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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
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Mathematica
b[_] = 0; a[n_] := a[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1]; Array[a, 105] (* Jean-François Alcover, Dec 20 2021 *) -
PARI
a(n)=my(d=numdiv(n)); sum(k=1,n,numdiv(k)==d) \\ Charles R Greathouse IV, Sep 02 2015
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