A072527 -id:A072527 - cp's OEIS frontend

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

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, 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, 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

Offset: 1

N. J. A. Sloane, Nov 04 2018

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.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000005, A001620, A321015.
A072527 is a shifted version.
Column k=4 of A135539.

d2:=proc(n) local c;
if n <= 3 then return(0); fi;
c:=NumberTheory[tau](n)-1;
if (n mod 2)=0 then c:=c-1; fi;
if (n mod 3)=0 then c:=c-1; fi; c; end;
[seq(d2(n),n=1..120)];

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

a(n) = sumdiv(n, d, d>3); \\ Michel Marcus, Nov 06 2018

a(n) = numdiv(n) - 3 + !!(n%2) + !!(n%3) \\ David A. Corneth, Nov 07 2018

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

G.f.: Sum_{k>=4} x^k/(1 - x^k). - Ilya Gutkovskiy, Nov 06 2018
a(n) = Sum_{d|n, d>3} 1. - Wesley Ivan Hurt, Apr 28 2020
G.f.: Sum_{k>=1} x^(4*k)/(1 - x^k). - Seiichi Manyama, Jan 07 2023
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

A072528 Table T(n,k) read by rows, giving number of occurrences of the remainder k when n is divided by i=1,2,3,...,n.

Original entry on oeis.org

1, 2, 2, 1, 3, 1, 2, 2, 1, 4, 1, 1, 2, 3, 1, 1, 4, 1, 2, 1, 3, 3, 1, 1, 1, 4, 2, 2, 1, 1, 2, 3, 2, 2, 1, 1, 6, 1, 2, 1, 1, 1, 2, 5, 1, 2, 1, 1, 1, 4, 1, 4, 1, 2, 1, 1, 4, 3, 1, 3, 1, 1, 1, 1, 5, 3, 2, 1, 2, 1, 1, 1, 2, 4, 3, 2, 1, 2, 1, 1, 1, 6, 1, 3, 2, 2, 1, 1, 1, 1, 2, 5, 1, 3, 2, 2, 1, 1, 1, 1, 6, 1, 4, 1, 2

Offset: 1

Amarnath Murthy, Aug 01 2002

The n-th row adds to n.

			The table begins
1
2
2 1
3 1
2 2 1
4 1 1
2 3 1 1
4 1 2 1

Cf. A023645 for T(n, 2) and A072527 for T(n, 3).

Cf. A230374, A230399.

Let a(m) be the m-th term in the sequence. Then m=f(n)+k where f(1)=1 and f(n+1)=f(n)+floor((n+1)/2). n is the number being divided by the various i's and k is the remainder under consideration. f(n) has the generating function F(x)= (x(1+2x^2-2x^3))/((1-x)^2(1+x^2)) - Bruce Corrigan (scentman(AT)myfamily.com), Oct 22 2002

G.f. for k-th column: Sum_{m>0} x^((k+1)*m+k)/(1-x^m). - Vladeta Jovovic, Dec 16 2002

Edited by Bruce Corrigan (scentman(AT)myfamily.com), Oct 22 2002

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 25 2003

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

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A072528 Table T(n,k) read by rows, giving number of occurrences of the remainder k when n is divided by i=1,2,3,...,n.

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