A049793 -id:A049793 - cp's OEIS frontend

A049790 Triangular array T read by rows: T(n,k) = Sum_{j=1..k} floor(n/floor(k/j)).

1, 2, 3, 3, 4, 7, 4, 6, 9, 11, 5, 7, 11, 13, 18, 6, 9, 14, 16, 22, 24, 7, 10, 16, 18, 25, 27, 34, 8, 12, 18, 22, 29, 31, 39, 43, 9, 13, 21, 24, 32, 35, 44, 47, 55, 10, 15, 23, 27, 37, 39, 49, 53, 61, 66, 11, 16, 25, 29, 40, 42, 53, 57, 66, 71, 82, 12, 18, 28, 33, 44, 48, 59, 64, 74, 79, 91, 94

Offset: 1

Clark Kimberling

			Triangle begins as:
  1;
  2,  3;
  3,  4,  7;
  4,  6,  9, 11;
  5,  7, 11, 13, 18;
  6,  9, 14, 16, 22, 24;
  7, 10, 16, 18, 25, 27, 34;
  8, 12, 18, 22, 29, 31, 39, 43;

G. C. Greubel, Rows n = 1..100 of triangle, flattened

Cf. A049791, A049792, A049793, A049794, A049795, A049796.

Flat(List([1..15], n-> List([1..n], k-> Sum([1..k], j-> Int(n/Int(k/j)) )))); # G. C. Greubel, Dec 09 2019

[(&+[Floor(n/Floor(k/j)): j in [1..k]]): k in [1..n], n in [1..15]]; // G. C. Greubel, Dec 09 2019

seq(seq( add(floor(n/floor(k/j)), j=1..k), k=1..n), n=1..15); # G. C. Greubel, Dec 09 2019

Table[Sum[Floor[n/Floor[k/j]], {j, k}], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Dec 09 2019 *)

T(n,k) = sum(j=1,k, n\(k\j));
for(n=1, 15, for(k=1, n, print1(T(n,k), ", "))) \\ G. C. Greubel, Dec 09 2019

[[sum(floor(n/floor(k/j)) for j in (1..k)) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Dec 09 2019

A049791 a(n) = Sum_{k=1..n} T(n,k), array T as in A049790.

Original entry on oeis.org

1, 5, 14, 30, 54, 91, 137, 202, 280, 380, 492, 644, 799, 994, 1212, 1471, 1735, 2071, 2400, 2811, 3232, 3709, 4190, 4804, 5380, 6046, 6739, 7535, 8297, 9246, 10115, 11153, 12184, 13320, 14458, 15839, 17074, 18493, 19931, 21583, 23100, 24942, 26609, 28564, 30517, 32593, 34585, 37048, 39231, 41735, 44187, 46911

Offset: 1

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A049790, A049792, A049793, A049794, A049795, A049796.

List([1..60], n-> Sum([1..n], k-> Sum([1..k], j-> Int(n/Int(k/j)) ))); # G. C. Greubel, Dec 10 2019

[ &+[(&+[Floor(n/Floor(k/j)): j in [1..k]]): k in [1..n]] n in [1..60]]; // G. C. Greubel, Dec 10 2019

seq( add(add(floor(n/floor(k/j)), j=1..k), k=1..n), n=1..60); # G. C. Greubel, Dec 10 2019

Table[Sum[Sum[Floor[n/Floor[k/j]], {j, k}], {k, n}], {n, 1, 60}] (* G. C. Greubel, Dec 10 2019 *)

a(n) = sum(k=1,n, sum(j=1,k, n\(k\j) ));
vector(60, n, a(n)) \\ G. C. Greubel, Dec 10 2019

[sum(sum(floor(n/floor(k/j)) for j in (1..k)) for k in (1..n)) for n in (1..60)] # G. C. Greubel, Dec 10 2019

Terms a(40) onward added by G. C. Greubel, Dec 10 2019

A049792 a(n) = Sum_{k=1..n} floor(n/floor(n/k)).

Original entry on oeis.org

1, 3, 7, 11, 18, 24, 34, 43, 55, 66, 82, 94, 113, 129, 150, 167, 192, 211, 239, 261, 290, 315, 349, 374, 410, 440, 478, 509, 552, 583, 629, 665, 711, 750, 802, 838, 893, 937, 992, 1036, 1097, 1141, 1205, 1255, 1317, 1370, 1440

Offset: 1

Clark Kimberling

nonn

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A049790, A049791, A049793, A049794, A049795, A049796.

List([1..60], n-> Sum([1..n], j-> Int(n/Int(n/j)) )); # G. C. Greubel, Dec 10 2019

[(&+[Floor(n/Floor(n/j)): j in [1..n]]): n in [1..60]]; // G. C. Greubel, Dec 10 2019

seq( add(floor(n/floor(n/j)), j=1..n), n=1..60); # G. C. Greubel, Dec 10 2019

Table[Total[Table[Quotient[n, Quotient[n, k]], {k, n}]], {n, 47}] (* Ivan Neretin, Jul 29 2015 *)

a(n) = sum(j=1,n, n\(n\j));
vector(60, n, a(n) ) \\ G. C. Greubel, Dec 10 2019

[sum(floor(n/floor(n/j)) for j in (1..n)) for n in (1..60)] # G. C. Greubel, Dec 10 2019

a(n) = A049790(n, n).
a(n) = A222548(n) - Sum_{i=1..n} floor(n/i)*floor(n/(i+1)). - Ridouane Oudra, Jun 22 2020
a(n) ~ (zeta(2) - 1) * n^2. - Vaclav Kotesovec, May 28 2021

A049794 a(n) = T(n,n-2), array T as in A049790.

Original entry on oeis.org

1, 2, 3, 6, 11, 16, 25, 31, 44, 53, 66, 79, 97, 108, 130, 148, 168, 187, 214, 233, 265, 286, 315, 344, 381, 402, 442, 474, 511, 545, 590, 619, 670, 705, 751, 797, 848, 880, 940, 988, 1041, 1087, 1150, 1192, 1263, 1311, 1370, 1431

Offset: 3

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 3..1000

Cf. A049790, A049791, A049792, A049793, A049795, A049796.

a:= function(n)
    if n<5 then return n-2;
    else return Sum([1..n-4], j-> Int((n-2)/Int((n-4)/j)) );
    fi; end;
List([3..60], n-> a(n) ); # G. C. Greubel, Dec 10 2019

[n lt 5 select n-2 else (&+[Floor((n-2)/Floor((n-4)/j)): j in [1..n-4]]): n in [3..60]]; // G. C. Greubel, Dec 10 2019

seq( `if`(n<5, n-2, add(floor((n-2)/floor((n-4)/j)), j=1..n-4)), n=3..60); # G. C. Greubel, Dec 10 2019

Table[If[n<5, n-2, Sum[Floor[(n-2)/Floor[(n-4)/j]], {j,n-4}]], {n, 3,60}] (* G. C. Greubel, Dec 10 2019 *)

a(n) = if(n<5, n-2, sum(j=1,n-4, (n-2)\((n-4)\j)) );
vector(60, n, a(n+2) ) \\ G. C. Greubel, Dec 10 2019

def a(n):
    if (n<5): return n-2
    else: return sum(floor((n-2)/floor((n-4)/j)) for j in (1..n-4))
[a(n) for n in (3..60)] # G. C. Greubel, Dec 10 2019

A049795 a(n) = T(n,n-3), array T as in A049790.

Original entry on oeis.org

1, 2, 3, 4, 7, 14, 18, 29, 35, 49, 57, 74, 84, 105, 115, 140, 155, 180, 195, 228, 244, 278, 296, 332, 356, 397, 416, 460, 487, 534, 559, 612, 637, 691, 722, 779, 814, 872, 901, 968, 1007, 1073, 1107, 1180, 1218, 1292, 1333, 1407

Offset: 4

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 4..1000

Cf. A049790, A049791, A049792, A049793, A049794, A049796.

a:= function(n)
    if n<7 then return n-3;
    else return Sum([1..n-6], j-> Int((n-3)/Int((n-6)/j)) );
    fi; end;
List([4..60], n-> a(n) ); # G. C. Greubel, Dec 10 2019

[n lt 7 select n-3 else (&+[Floor((n-3)/Floor((n-6)/j)): j in [1..n-6]]): n in [4..60]]; // G. C. Greubel, Dec 10 2019

seq( `if`(n<7, n-3, add(floor((n-3)/floor((n-6)/j)), j=1..n-6)), n=4..60); # G. C. Greubel, Dec 10 2019

Table[If[n<7, n-3, Sum[Floor[(n-3)/Floor[(n-6)/j]], {j,n-6}]], {n,4,60}] (* G. C. Greubel, Dec 10 2019 *)

a(n) = if(n<7, n-3, sum(j=1,n-6, (n-3)\((n-6)\j)) );
vector(60, n, a(n+3) ) \\ G. C. Greubel, Dec 10 2019

def a(n):
    if (n<7): return n-3
    else: return sum(floor((n-3)/floor((n-6)/j)) for j in (1..n-6))
[a(n) for n in (4..60)] # G. C. Greubel, Dec 10 2019

A049796 a(n) = T(n,n-4), array T as in A049790.

Original entry on oeis.org

1, 2, 3, 4, 5, 9, 16, 22, 32, 39, 53, 64, 79, 91, 113, 124, 147, 166, 188, 208, 238, 256, 288, 313, 344, 371, 411, 434, 473, 509, 548, 580, 629, 657, 709, 749, 796, 837, 893, 928, 987, 1038, 1093, 1136, 1206, 1246, 1314, 1371, 1431

Offset: 5

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 5..1000

Cf. A049790, A049791, A049792, A049793, A049794, A049795.

a:= function(n)
    if n<9 then return n-4;
    else return Sum([1..n-8], j-> Int((n-4)/Int((n-8)/j)) );
    fi; end;
List([5..60], n-> a(n) ); # G. C. Greubel, Dec 10 2019

[n lt 9 select n-4 else (&+[Floor((n-4)/Floor((n-8)/j)): j in [1..n-8]]): n in [5..60]]; // G. C. Greubel, Dec 10 2019

seq( `if`(n<9, n-4, add(floor((n-4)/floor((n-8)/j)), j=1..n-8)), n=5..60); # G. C. Greubel, Dec 10 2019

Table[If[n<9, n-4, Sum[Floor[(n-4)/Floor[(n-8)/j]], {j,n-8}]], {n,5,60}] (* G. C. Greubel, Dec 10 2019 *)

a(n) = if(n<9, n-4, sum(j=1,n-8, (n-4)\((n-8)\j)) );
vector(60, n, a(n+4) ) \\ G. C. Greubel, Dec 10 2019

def a(n):
    if (n<9): return n-4
    else: return sum(floor((n-4)/floor((n-8)/j)) for j in (1..n-8))
[a(n) for n in (5..60)] # G. C. Greubel, Dec 10 2019

cp's OEIS Frontend

A049790 Triangular array T read by rows: T(n,k) = Sum_{j=1..k} floor(n/floor(k/j)).

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A049791 a(n) = Sum_{k=1..n} T(n,k), array T as in A049790.

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A049792 a(n) = Sum_{k=1..n} floor(n/floor(n/k)).

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A049794 a(n) = T(n,n-2), array T as in A049790.

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GAP

Magma

Maple

Mathematica

PARI

Sage

A049795 a(n) = T(n,n-3), array T as in A049790.

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GAP

Magma

Maple

Mathematica

PARI

Sage

A049796 a(n) = T(n,n-4), array T as in A049790.

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Programs

GAP

Magma

Maple

Mathematica