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Numbers n such that tau(n) is different from tau(n-1), where tau(m) = number of divisors of m.
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%I #13 Dec 24 2014 10:51:03

%S 1,2,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,23,24,25,26,28,29,

%T 30,31,32,33,36,37,38,40,41,42,43,44,46,47,48,49,50,51,52,53,54,55,56,

%U 57,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,77,78,79,80,81,82

%N Numbers n such that tau(n) is different from tau(n-1), where tau(m) = number of divisors of m.

%H Michael De Vlieger, <a href="/A083794/b083794.txt">Table of n, a(n) for n = 1..10000</a>

%H P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1936-03.pdf">On a problem of Chowla and some related problems</a>, Proc. Cambridge Philos. Soc. 32 (1936), pp. 530-540.

%F Erdős proved that a(n) ~ n. - _Charles R Greathouse IV_, Dec 05 2012

%p with(numtheory): for n from 1 to 150 do if tau(n) <> tau(n-1) then printf(`%d,`,n) fi: od: # _James A. Sellers_, May 19 2003

%t a083794[n_] :=

%t Prepend[Select[Range[1, n],

%t DivisorSigma[0, #] != DivisorSigma[0, # - 1] &], 1]; a083794[82] (* _Michael De Vlieger_, Dec 24 2014 *)

%o (PARI) is(n)=numdiv(n-1)!=numdiv(n)

%Y Cf. A083795.

%K nonn

%O 1,2

%A _Amarnath Murthy_, May 07 2003

%E More terms from _James A. Sellers_, May 19 2003