cp's OEIS Frontend

A067004 Number of numbers <= n with same number of divisors as n.

%I A067004 #18 Dec 20 2021 18:36:38
%S A067004 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,
%T A067004 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,
%U A067004 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
%N A067004 Number of numbers <= n with same number of divisors as n.
%H A067004 Paul Tek, <a href="/A067004/b067004.txt">Table of n, a(n) for n = 1..10000</a>
%F A067004 Ordinal transform of A000005. - _Franklin T. Adams-Watters_, Aug 28 2006
%F A067004 a(A000040(n)^(p-1)) = n if p is prime. - _Robert Israel_, May 04 2015
%e A067004 a(10)=3 since 6,8,10 each have four divisors. a(11)=5 since 2,3,5,7,11 each have two divisors.
%p A067004 N:= 1000: # to get a(1) to a(N)
%p A067004 R:= Vector(N):
%p A067004 for n from 1 to N do
%p A067004   v:= numtheory:-tau(n);
%p A067004   R[v]:= R[v]+1;
%p A067004   A[n]:= R[v];
%p A067004 od:
%p A067004 seq(A[n],n=1..N); # _Robert Israel_, May 04 2015
%t A067004 b[_] = 0;
%t A067004 a[n_] := a[n] = With[{t = DivisorSigma[0, n]}, b[t] = b[t]+1];
%t A067004 Array[a, 105] (* _Jean-François Alcover_, Dec 20 2021 *)
%o A067004 (PARI) a(n)=my(d=numdiv(n)); sum(k=1,n,numdiv(k)==d) \\ _Charles R Greathouse IV_, Sep 02 2015
%Y A067004 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.
%Y A067004 Cf. also A079788, A138009.
%Y A067004 A047983(n) = a(n)-1.
%K A067004 nonn
%O A067004 1,3
%A A067004 _Henry Bottomley_, Dec 21 2001