A321014 - OEIS

%I #33 Sep 30 2025 19:25:41

%S 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 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 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 Number of divisors of n which are greater than 3.

%D 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 Seiichi Manyama, <a href="/A321014/b321014.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=4} x^k/(1 - x^k). - _Ilya Gutkovskiy_, Nov 06 2018

%F a(n) = Sum_{d|n, d>3} 1. - _Wesley Ivan Hurt_, Apr 28 2020

%F G.f.: Sum_{k>=1} x^(4*k)/(1 - x^k). - _Seiichi Manyama_, Jan 07 2023

%F 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 d2:=proc(n) local c;

%p if n <= 3 then return(0); fi;

%p c:=NumberTheory[tau](n)-1;

%p if (n mod 2)=0 then c:=c-1; fi;

%p if (n mod 3)=0 then c:=c-1; fi; c; end;

%p [seq(d2(n),n=1..120)];

%t nmax = 94; Rest[CoefficientList[Series[Sum[x^k/(1 - x^k), {k, 4, nmax}], {x, 0, nmax}], x]] (* _Ilya Gutkovskiy_, Nov 07 2018 *)

%t Table[Count[Divisors[n],_?(#>3&)],{n,100}] (* _Harvey P. Dale_, Sep 30 2025 *)

%o (PARI) a(n) = sumdiv(n, d, d>3); \\ _Michel Marcus_, Nov 06 2018

%o (PARI) a(n) = numdiv(n) - 3 + !!(n%2) + !!(n%3) \\ _David A. Corneth_, Nov 07 2018

%o (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 Cf. A000005, A001620, A321015.

%Y A072527 is a shifted version.

%Y Column k=4 of A135539.

%K nonn,easy

%O 1,8

%A _N. J. A. Sloane_, Nov 04 2018