cp's OEIS Frontend

A072527 Number of values of k such that n divided by k leaves a remainder 3.

%I A072527 #27 Jan 18 2024 04:24:58
%S A072527 0,0,0,0,0,0,1,1,1,1,2,1,2,1,3,1,2,2,3,1,3,1,4,2,2,1,5,2,2,2,4,1,5,1,
%T A072527 4,2,2,3,6,1,2,2,6,1,5,1,4,4,2,1,7,2,4,2,4,1,5,3,6,2,2,1,9,1,2,4,5,3,
%U A072527 5,1,4,2,6,1,9,1,2,4,4,3,5,1,8,3,2,1,9,3,2,2,6,1,9,3,4,2,2,3,9,1,4,4,7,1,5
%N A072527 Number of values of k such that n divided by k leaves a remainder 3.
%C A072527 For n > 3, the number of divisors of (n - 3) that are greater than 3; equivalently, those that are less than (n - 3)/3. - _Peter Munn_, May 18 2017
%H A072527 Paolo Xausa, <a href="/A072527/b072527.txt">Table of n, a(n) for n = 1..10000</a>
%F A072527 a(n) = tau(n-3)-1 if n is congruent to {2, 4} mod 6, tau(n-3)-2 if n is congruent to {0, 1, 5} mod 6, tau(n-3)-3 if n is congruent to 3 mod 6; n<>3. - _Vladeta Jovovic_, Aug 06 2002
%F A072527 G.f.: Sum_{k>0} x^(4*k+3)/(1-x^k). - _Vladeta Jovovic_, Dec 15 2002
%F A072527 Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 17/6), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Jan 18 2024
%e A072527 a(15) = 3 as 15 divided by exactly three numbers 4, 6 and 12 leaves a remainder 3.
%t A072527 A072527[n_] := If[n>6, DivisorSum[n-3, 1&, #>3&], 0];
%t A072527 Array[A072527, 150] (* _Paolo Xausa_, Jan 18 2024 *)
%o A072527 (PARI) a(n) = sum(k=1, n-1, (n % k) == 3); \\ _Michel Marcus_, May 25 2017
%o A072527 (PARI) a(n)=if(n>6, numdiv(n-3) - if(n%6==3, 3, if(n%6==2 || n%6==4, 1, 2)), 0) \\ _Charles R Greathouse IV_, May 27 2017
%Y A072527 Cf. A001620, A023645, A072528.
%K A072527 nonn,easy
%O A072527 1,11
%A A072527 _Amarnath Murthy_, Aug 01 2002
%E A072527 More terms from _Matthew Conroy_, Sep 09 2002
%E A072527 Incorrect comment deleted by _Peter Munn_, May 25 2017