A135539 -id:A135539 - cp's OEIS frontend

A338649 Number of divisors of n which are greater than 5.

0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 5, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 7, 1, 2, 4, 4, 2, 5, 1, 3, 2, 5, 1, 8, 1, 2, 3, 3, 3, 5, 1, 6, 3, 2, 1, 8, 2, 2, 2, 5, 1, 8, 3, 3, 2, 2, 2, 8, 1, 4, 4, 5, 1, 5, 1, 5, 5, 2, 1, 8, 1, 5

Offset: 1

Ilya Gutkovskiy, Apr 22 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to divisors of numbers.

Column k=6 of A135539.

Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338650, A338651, A338652, A338653.

Table[DivisorSum[n, 1 &, # > 5 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(6 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 6, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &

a(n) = sumdiv(n, d, d>5); \\ Michel Marcus, Apr 22 2021

my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0], Vec(sum(k=6, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

G.f.: Sum_{k>=1} x^(6*k) / (1 - x^k).
L.g.f.: -log( Product_{k>=6} (1 - x^k)^(1/k) ).
G.f.: Sum_{k>=6} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 197/60), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

a(1)-a(5) prepended by David A. Corneth, Jun 13 2022

A064944 a(n) = Sum_{i|n, j|n, j >= i} j.

Original entry on oeis.org

1, 5, 7, 17, 11, 38, 15, 49, 34, 60, 23, 132, 27, 82, 82, 129, 35, 191, 39, 207, 112, 126, 47, 384, 86, 148, 142, 283, 59, 469, 63, 321, 172, 192, 172, 666, 75, 214, 202, 597, 83, 640, 87, 435, 403, 258, 95, 1016, 162, 485, 262, 511, 107, 812, 264, 813, 292, 324

Offset: 1

Vladeta Jovovic, Oct 28 2001

nonn

			a(6) = max(1,1)+max(1,2)+max(1,3)+max(1,6)+max(2,2)+max(2,3)+max(2,6)+max(3,3)+max(3,6)+max(6,6)=38, or a(6) = dot_product(1,2,3,4)*(1,2,3,6)=1*1+2*2+3*3+4*6=38.

Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harry J. Smith)

Cf. A060640, A064945, A064946, A064947, A064948, A064949.

Cf. A027750, A135539, A000005, A000203, A064840, A337360, A337297.

a064944 = sum . zipWith (*) [1..] . a027750_row'
-- Reinhard Zumkeller, Jul 14 2015

with(numtheory): seq(add(i*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);

A064944[n_] := #.Range[Length[#]] & [Divisors[n]];
Array[A064944, 100] (* Paolo Xausa, Aug 07 2025 *)

a(n) = my(d=divisors(n)); sum(i=1, length(d), i*d[i]); \\ Harry J. Smith, Sep 30 2009

from sympy import divisors
def A064944(n): return sum(a*b for a, b in enumerate(divisors(n),1)) # Chai Wah Wu, Aug 07 2025

a(n) = Sum_{i=1..tau(n)} i*d_i, where {d_i}, i=1..tau(n) is the increasing sequence of divisors of n.
a(n) = Sum_{i=1..A000005(n)} i*A027750(n, i). - Michel Marcus, Jun 10 2015
From Ridouane Oudra, Aug 01 2025: (Start)
a(n) = Sum_{d|n} (n/d)*A135539(n,d).
a(n) = A064946(n) + A000203(n).
a(n) = (A064948(n) + A000203(n))/2.
a(n) = A337360(n) - A064945(n).
a(n) = A064948(n) - A064946(n).
a(n) = A064840(n) - A064947(n). (End)

A338650 Number of divisors of n which are greater than 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 5, 2, 3, 2, 3, 1, 4, 2, 5, 2, 2, 1, 6, 1, 2, 4, 4, 2, 4, 1, 3, 2, 5, 1, 7, 1, 2, 3, 3, 3, 4, 1, 6, 3, 2, 1, 7, 2, 2, 2, 5, 1, 7, 3, 3, 2, 2, 2, 7, 1, 4, 4, 5, 1, 4, 1, 5, 5, 2, 1, 7, 1, 5

Offset: 1

Ilya Gutkovskiy, Apr 22 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to divisors of numbers.

Column k=7 of A135539.

Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338649, A338651, A338652, A338653.

Table[DivisorSum[n, 1 &, # > 6 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(7 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 7, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &

a(n) = sumdiv(n, d, d>6); \\ Michel Marcus, Apr 22 2021

my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0], Vec(sum(k=7, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

G.f.: Sum_{k>=1} x^(7*k) / (1 - x^k).
L.g.f.: -log( Product_{k>=7} (1 - x^k)^(1/k) ).
G.f.: Sum_{k>=7} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 69/20), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

a(1)-a(6) prepended by David A. Corneth, Jun 13 2022

A338651 Number of divisors of n which are greater than 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 1, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 6, 1, 2, 3, 4, 2, 4, 1, 3, 2, 4, 1, 7, 1, 2, 3, 3, 2, 4, 1, 6, 3, 2, 1, 6, 2, 2, 2, 5, 1, 7, 2, 3, 2, 2, 2, 7, 1, 3, 4, 5, 1, 4, 1, 5, 4, 2, 1, 7, 1, 5

Offset: 1

Ilya Gutkovskiy, Apr 22 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to divisors of numbers.

Column k=8 of A135539.

Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338649, A338650, A338652, A338653.

Table[DivisorSum[n, 1 &, # > 7 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(8 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 8, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &

a(n) = sumdiv(n, d, d>7); \\ Michel Marcus, Apr 22 2021

my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0, 0], Vec(sum(k=8, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

G.f.: Sum_{k>=1} x^(8*k) / (1 - x^k).
L.g.f.: -log( Product_{k>=8} (1 - x^k)^(1/k) ).
G.f.: Sum_{k>=8} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 503/140), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

a(1)-a(7) prepended by David A. Corneth, Jun 13 2022

A338652 Number of divisors of n which are greater than 8.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 4, 1, 3, 2, 3, 1, 4, 2, 3, 2, 2, 1, 6, 1, 2, 3, 3, 2, 4, 1, 3, 2, 4, 1, 6, 1, 2, 3, 3, 2, 4, 1, 5, 3, 2, 1, 6, 2, 2, 2, 4, 1, 7, 2, 3, 2, 2, 2, 6, 1, 3, 4, 5, 1, 4, 1, 4, 4, 2, 1, 7, 1, 5

Offset: 1

Ilya Gutkovskiy, Apr 22 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to divisors of numbers.

Column k=9 of A135539.

Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338649, A338650, A338651, A338653.

Table[DivisorSum[n, 1 &, # > 8 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(9 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 9, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &

a(n) = sumdiv(n, d, d>8); \\ Michel Marcus, Apr 22 2021

my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0, 0, 0], Vec(sum(k=9, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

G.f.: Sum_{k>=1} x^(9*k) / (1 - x^k).
L.g.f.: -log( Product_{k>=9} (1 - x^k)^(1/k) ).
G.f.: Sum_{k>=9} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 1041/280), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

a(1)-a(8) prepended by David A. Corneth, Jun 13 2022

A338653 Number of divisors of n which are greater than 9.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 3, 1, 3, 2, 2, 1, 4, 1, 3, 2, 3, 1, 3, 2, 3, 2, 2, 1, 6, 1, 2, 2, 3, 2, 4, 1, 3, 2, 4, 1, 5, 1, 2, 3, 3, 2, 4, 1, 5, 2, 2, 1, 6, 2, 2, 2, 4, 1, 6, 2, 3, 2, 2, 2, 6, 1, 3, 3, 5, 1, 4, 1, 4, 4, 2, 1, 6, 1, 5

Offset: 1

Ilya Gutkovskiy, Apr 22 2021

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Index entries for sequences related to divisors of numbers.

Column k=10 of A135539.

Cf. A000005, A001620, A023645, A032741, A321014, A338648, A338649, A338650, A338651, A338652.

Table[DivisorSum[n, 1 &, # > 9 &], {n, 1, 110}]
nmax = 110; CoefficientList[Series[Sum[x^(10 k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Drop[#, 1] &
nmax = 110; CoefficientList[Series[-Log[Product[(1 - x^k)^(1/k), {k, 10, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Drop[#, 1] &
Table[Count[Divisors[n],?(#>9&)],{n,120}] (* _Harvey P. Dale, Jan 09 2025 *)

a(n) = sumdiv(n, d, d>9); \\ Michel Marcus, Apr 22 2021

my(N=100, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0, 0, 0, 0], Vec(sum(k=10, N, x^k/(1-x^k)))) \\ Seiichi Manyama, Jan 07 2023

G.f.: Sum_{k>=1} x^(10*k) / (1 - x^k).
L.g.f.: -log( Product_{k>=10} (1 - x^k)^(1/k) ).
G.f.: Sum_{k>=10} x^k/(1 - x^k). - Seiichi Manyama, Jan 07 2023
Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 9649/2520), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 08 2024

a(1)-a(9) prepended by David A. Corneth, Jun 13 2022

A064949 a(n) = Sum_{i|n, j|n} min(i,j).

Original entry on oeis.org

1, 5, 6, 15, 8, 32, 10, 37, 23, 42, 14, 100, 16, 52, 52, 83, 20, 125, 22, 132, 64, 72, 26, 252, 45, 82, 76, 162, 32, 286, 34, 177, 88, 102, 88, 397, 40, 112, 100, 336, 44, 352, 46, 222, 208, 132, 50, 572, 75, 239, 124, 252, 56, 416, 120, 414, 136, 162, 62, 916, 64

Offset: 1

Vladeta Jovovic, Oct 28 2001

nonn

			a(6) = dot_product(7,5,3,1)*(1,2,3,6) = 7*1 + 5*2 + 3*3 + 1*6 = 32.

Antti Karttunen, Table of n, a(n) for n = 1..20000 (first 1000 terms from Harry J. Smith)

Cf. A000005, A000203, A064944, A064945, A135539, A064840.

with(numtheory): seq(add((2*tau(n)-2*i+1)*sort(convert(divisors(n),'list'))[i],i=1..tau(n)), n=1..200);

Array[Function[{t, d}, Total@ MapIndexed[#1 (2 t - 2 First[#2] + 1) &, d]] @@ {DivisorSigma[0, #], Divisors[#]} &, 61] (* Michael De Vlieger, Oct 25 2021 *)

a(n) = { my(d=divisors(n), t=length(d)); sum(i=1, t, (2*t - 2*i + 1)*d[i]) } \\ Harry J. Smith, Oct 01 2009

A064949(n) = { my(i=0, u=numdiv(n)); sumdiv(n,d,i++; (((2*u)-(2*i))+1)*d); }; \\ Antti Karttunen, Nov 14 2021

a(n) = Sum_{i=1..tau(n)} (2*tau(n)-2*i+1)*d_i, where {d_i}, i=1..tau(n), is increasing sequence of divisors of n.
a(n) = Sum_{i=1..n} A135539(n,i)^2. - Ridouane Oudra, Oct 25 2021
a(n) = A000203(n) * (2*A000005(n)+1) - 2*A064944(n). - Amiram Eldar, Jan 13 2025
From Ridouane Oudra, Aug 13 2025: (Start)
a(n) = A064945(n) + A064947(n).
a(n) = 2*A064947(n) + A000203(n).
a(n) = 2*A064945(n) - A000203(n).
a(n) = 2*A064840(n) - A064948(n). (End)

A182627 Total number of digits in binary expansion of all divisors of n.

Original entry on oeis.org

1, 3, 3, 6, 4, 8, 4, 10, 7, 10, 5, 15, 5, 10, 10, 15, 6, 17, 6, 18, 11, 12, 6, 24, 9, 12, 12, 18, 6, 24, 6, 21, 13, 14, 13, 30, 7, 14, 13, 28, 7, 26, 7, 21, 20, 14, 7, 35, 10, 21, 14, 21, 7, 28, 14, 28, 14, 14, 7, 42, 7, 14, 21, 28, 15, 30, 8, 24, 15, 30, 8

Offset: 1

Omar E. Pol, Nov 23 2010

Also, total number of digits in row n of triangle A182620.
Also, number of digits of A182621(n).
Rows sums of triangle A182628.
From Davide Rotondo, Apr 20 2022: (Start)
Can be constructed by writing the sequence of natural numbers with 1 one, 2 twos, 4 threes, 8 fours, ..., where 1,2,4,8,... are consecutive powers of 2; then the same sequence spaced by a zero, then the same sequence spaced by two zeros, and so on. Finally add the values of the columns.
     1  2  2  3  3  3  3  4  4  4  4  4  4  4  4  5 ...
     0  1  0  2  0  2  0  3  0  3  0  3  0  3  0  4 ...
     0  0  1  0  0  2  0  0  2  0  0  3  0  0  3  0 ...
     0  0  0  1  0  0  0  2  0  0  0  2  0  0  0  3 ...
     0  0  0  0  1  0  0  0  0  2  0  0  0  0  2  0 ...
     0  0  0  0  0  1  0  0  0  0  0  2  0  0  0  0 ...
     0  0  0  0  0  0  1  0  0  0  0  0  0  2  0  0 ...
     0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  2 ...
     0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0 ...
     0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0 ...
     0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0 ...
     0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0 ...
     0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0 ...
     0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0 ...
     0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0 ...
     0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1 ...
     ...
     ----------------------------------------------
Tot. 1  3  3  6  4  8  4 10  7 10  5 15  5 10 10 15 ...  (End)

			The divisors of 12 are 1, 2, 3, 4, 6, 12. These divisors written in base 2 are 1, 10, 11, 100, 110, 1100. Then a(12)=15 because 1+2+2+3+3+4 = 15.

Jaroslav Krizek, Table of n, a(n) for n = 1..500

Cf. A093653, A135539, A182620, A182621, A182628.
Cf. A093653 (number of 1's in binary expansion of all divisors of n).
Cf. A226590 (number of 0's in binary expansion of all divisors of n).

Table[Total[IntegerLength[Divisors[n],2]],{n,60}] (* Harvey P. Dale, Jan 26 2012 *)

a(n) = sumdiv(n, d, 1+logint(d, 2)); \\ Michel Marcus, Dec 11 2020

from sympy import divisors
def a(n): return sum(d.bit_length() for d in divisors(n))
print([a(n) for n in range(1, 72)]) # Michael S. Branicky, Apr 21 2022

a(n) = A093653(n) + A226590(n). - Jaroslav Krizek, Sep 01 2013
a(n) = tau(n) + Sum_{d|n} floor(log_2(d)). - Ridouane Oudra, Dec 11 2020
a(n) = Sum_{i=0..floor(log_2(n))} A135539(n,2^i). - Ridouane Oudra, Sep 19 2022

A130887 Inverse Moebius transform of the Mersenne numbers: a(n) = Sum_{d|n} (2^d - 1).

Original entry on oeis.org

1, 4, 8, 19, 32, 74, 128, 274, 519, 1058, 2048, 4184, 8192, 16514, 32806, 65809, 131072, 262728, 524288, 1049648, 2097286, 4196354, 8388608, 16781654, 33554463, 67117058, 134218246, 268451984, 536870912, 1073775718, 2147483648, 4295033104, 8589936646

Offset: 1

Gary W. Adamson, Jun 07 2007

nonn

			G.f. = x + 4*x^2 + 8*x^3 + 19*x^4 + 32*x^5 + 74*x^6 + 128*x^7 + 274*x^8 + ...

Enrique Pérez Herrero, Table of n, a(n) for n = 1..500

Cf. A001047.

Cf. A027750, A000225, A038199.

a130887 = sum . map a000225 . a027750_row
-- Reinhard Zumkeller, Feb 17 2013

A130887[n_]:=DivisorSum[n,Plus@@Table[Binomial[#,i],{i,1,#}]&]; Array[A130887,20] (* Enrique Pérez Herrero, Apr 14 2012 *)
a[ n_] := If[ n < 1, 0, DivisorSum[ n, 2^# - 1 &]]; (* Michael Somos, Jan 28 2017 *)

{a(n) = if( n<1, 0, sumdiv(n, d, 2^d-1))}; /* Michael Somos, Jan 28 2017 */

a(n) = Sum_{d|n} Sum_{k=1..d} C(d,k) = Sum_{d|n} (-1 + 2^d) = Sum_{d|n} 2^d - tau(n) = A055895(n) - A000010(n). - Enrique Pérez Herrero, Apr 14 2012
G.f.: Sum_{k>=1} (2^k - 1)*x^k/(1 - x^k). - Ilya Gutkovskiy, Jan 28 2017
a(n) = Sum_{i=1..n} 2^(i-1)*A135539(n,i). - Ridouane Oudra, Sep 19 2022

New name from Enrique Pérez Herrero, Apr 14 2012

Name corrected by Michel Marcus, Sep 19 2022

A134867 A010766 * A000012.

Original entry on oeis.org

1, 3, 1, 5, 2, 1, 8, 4, 2, 1, 10, 5, 3, 2, 1, 14, 8, 5, 3, 2, 1, 16, 9, 6, 4, 3, 2, 1, 20, 12, 8, 6, 4, 3, 2, 1, 23, 14, 10, 7, 5, 4, 3, 2, 1, 27, 17, 12, 9, 7, 5, 4, 3, 2, 1, 29, 18, 13, 10, 8, 6, 5, 4, 3, 2, 1, 35, 23, 17, 13, 10, 8, 6, 5, 4, 3, 2, 1, 37, 24, 18, 14, 11, 9, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Gary W. Adamson, Nov 14 2007

			First few rows of the triangle:
   1;
   3,  1;
   5,  2,  1;
   8,  4,  2, 1;
  10,  5,  3, 2, 1;
  14,  8,  5, 3, 2, 1;
  16,  9,  6, 4, 3, 2, 1;
  20, 12,  8, 6, 4, 3, 2, 1;
  23, 14, 10, 7, 5, 4, 3, 2, 1;
  27, 17, 12, 9, 7, 5, 4, 3, 2, 1;
  ...

Column k=1..4 give: A006218, A002541, A366968, A366972.
Row sums give A024916.
Cf. A010766, A135539.

t = Table[Sum[Floor[n/h], {h, k, n}], {n, 0, 10}, {k, 1, n}];
u = Flatten[t]  (* A134867 array *)
TableForm[t]    (* A134867 sequence *)
(* Clark Kimberling, Oct 11 2014 *)

T(n, k) = sum(j=k, n, n\j); \\ Seiichi Manyama, Oct 30 2023

A010766 * A000012 as infinite lower triangular matrices.
Triangle read by rows, partial row sums of A010766 starting fromt the right.
G.f. of column k: 1/(1-x) * Sum_{j>=1} x^(k*j)/(1-x^j) = 1/(1-x) * Sum_{j>=k} x^j/(1-x^j). - Seiichi Manyama, Oct 30 2023

More terms from Seiichi Manyama, Oct 30 2023

cp's OEIS Frontend

A338649 Number of divisors of n which are greater than 5.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A064944 a(n) = Sum_{i|n, j|n, j >= i} j.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

PARI

Python

Formula

A338650 Number of divisors of n which are greater than 6.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A338651 Number of divisors of n which are greater than 7.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A338652 Number of divisors of n which are greater than 8.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A338653 Number of divisors of n which are greater than 9.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A064949 a(n) = Sum_{i|n, j|n} min(i,j).

Views

Author

Keywords

Examples