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A321014 Number of divisors of n which are greater than 3.

%I A321014 #31 Jan 08 2024 01:36:26
%S A321014 0,0,0,1,1,1,1,2,1,2,1,3,1,2,2,3,1,3,1,4,2,2,1,5,2,2,2,4,1,5,1,4,2,2,
%T A321014 3,6,1,2,2,6,1,5,1,4,4,2,1,7,2,4,2,4,1,5,3,6,2,2,1,9,1,2,4,5,3,5,1,4,
%U A321014 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
%N A321014 Number of divisors of n which are greater than 3.
%D A321014 Marjorie Senechal, "Introduction to lattice geometry." In M. Waldschmidt et al., eds., From Number Theory to Physics, pp. 476-495. Springer, Berlin, Heidelberg, 1992. See Cor. 3.7.
%H A321014 Seiichi Manyama, <a href="/A321014/b321014.txt">Table of n, a(n) for n = 1..10000</a>
%F A321014 G.f.: Sum_{k>=4} x^k/(1 - x^k). - _Ilya Gutkovskiy_, Nov 06 2018
%F A321014 a(n) = Sum_{d|n, d>3} 1. - _Wesley Ivan Hurt_, Apr 28 2020
%F A321014 G.f.: Sum_{k>=1} x^(4*k)/(1 - x^k). - _Seiichi Manyama_, Jan 07 2023
%F A321014 Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 17/6), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Jan 08 2024
%p A321014 d2:=proc(n) local c;
%p A321014 if n <= 3 then return(0); fi;
%p A321014 c:=NumberTheory[tau](n)-1;
%p A321014 if (n mod 2)=0 then c:=c-1; fi;
%p A321014 if (n mod 3)=0 then c:=c-1; fi; c; end;
%p A321014 [seq(d2(n),n=1..120)];
%t A321014 nmax = 94; Rest[CoefficientList[Series[Sum[x^k/(1 - x^k), {k, 4, nmax}], {x, 0, nmax}], x]] (* _Ilya Gutkovskiy_, Nov 07 2018 *)
%o A321014 (PARI) a(n) = sumdiv(n, d, d>3); \\ _Michel Marcus_, Nov 06 2018
%o A321014 (PARI) a(n) = numdiv(n) - 3 + !!(n%2) + !!(n%3) \\ _David A. Corneth_, Nov 07 2018
%o A321014 (PARI) my(N=100, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^(4*k)/(1-x^k)))) \\ _Seiichi Manyama_, Jan 07 2023
%Y A321014 Cf. A000005, A001620, A321015.
%Y A321014 A072527 is a shifted version.
%Y A321014 Column k=4 of A135539.
%K A321014 nonn,easy
%O A321014 1,8
%A A321014 _N. J. A. Sloane_, Nov 04 2018