A341627 Square array A(n,k) = A341527(A246278(n,k)), read by falling antidiagonals; denominators of the columnwise first quotients of A341605/A341606.

9, 63, 10, 5, 325, 21, 81, 7, 1519, 22, 189, 1250, 11, 363, 78, 35, 220, 13377, 52, 22477, 119, 33, 455, 117, 66550, 34, 52887, 171, 2511, 260, 4774, 374, 804102, 133, 110827, 115, 325, 6875, 833, 2574, 6669, 584647, 69, 201549, 116, 1323, 3038, 1875181, 627, 205751, 13685, 1790199, 58, 465073, 465

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

A(n,k) = A341527(A246278(n,k)), where A341527(n) is the denominator of the ratio (n * sigma(A003961(n))) / (sigma(n) * A003961(n)), i.e., of A341528(n)/A341529(n).

For all n, k, A(n,k) > A341626(n, k).

Example

The top left corner of the array:
   n =  1       2    3        4      5        6      7             8        9
  2n =  2       4    6        8     10       12     14            16       18
----+--------------------------------------------------------------------------
  1 |   9,     63,   5,      81,   189,      35,    33,         2511,     325,
  2 |  10,    325,   7,    1250,   220,     455,   260,         6875,    3038,
  3 |  21,   1519,  11,   13377,   117,    4774,   833,      1875181,    1089,
  4 |  22,    363,  52,   66550,   374,    2574,   627,     41009441,    6422,
  5 |  78,  22477,  34,  804102,  6669,  205751,  1495,    459974905,  317322,
  6 | 119,  52887, 133,  584647, 13685,  531981, 13804,   2584223261,  775789,
  7 | 171, 110827,  69, 1790199,  9918,  670795, 15903,  11564815861, 1813941,
  8 | 115, 201549,  58, 2202227, 17825, 1016508, 34040,  38495207801, 2325365,
  9 | 116, 465073,  93, 5170468, 68672, 7457205, 90364, 206922836641, 3348124,
etc.

Prog

(PARI)
up_to = 105;
A246278sq(row, col) = if(1==row, 2*col, my(f = factor(2*col)); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));
A341627sq(row, col) = A341527(A246278sq(row, col));
A341627list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A341627sq(col, (a-(col-1))))); (v); };
v341627 = A341627list(up_to);
A341627(n) = v341627[n];

Crossrefs

Cf. A246278, A341605, A341606, A341527.

Cf. A341626 (numerators), A341628 (the greatest prime factor of these terms).

Sequence in context: A346396 A240391 A229701 * A159235 A181403 A292309

Adjacent sequences: A341624 A341625 A341626 * A341628 A341629 A341630

Keyword

nonn,frac,tabl

Author

Antti Karttunen, Feb 16 2021

Status

approved