A341626 Square array A(n,k) = A341526(A246278(n,k)), read by falling antidiagonals; Numerators of the columnwise first quotients of A341605/A341606.

8, 52, 9, 4, 279, 20, 64, 6, 1425, 21, 160, 1053, 10, 343, 77, 26, 189, 12500, 49, 22143, 117, 28, 372, 110, 62769, 33, 51883, 170, 1936, 231, 4275, 351, 791945, 130, 110109, 114, 248, 5751, 780, 2401, 6545, 573417, 68, 199633, 115, 1040, 2565, 1750625, 595, 199287, 13338, 1778506, 57, 460759, 464

Offset: 1

Author

Antti Karttunen, Feb 16 2021

Keywords

• nonn
• frac
• tabl

Comments

See comments in A341605.

Examples

			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 |   8,     52,   4,      64,   160,      26,    28,         1936,     248,
  2 |   9,    279,   6,    1053,   189,     372,   231,         5751,    2565,
  3 |  20,   1425,  10,   12500,   110,    4275,   780,      1750625,     980,
  4 |  21,    343,  49,   62769,   351,    2401,   595,     38668105,    6039,
  5 |  77,  22143,  33,  791945,  6545,  199287,  1463,    453007181,  307307,
  6 | 117,  51883, 130,  573417, 13338,  518830, 13455,   2534531701,  757809,
  7 | 170, 110109,  68, 1778506,  9775,  660654, 15776,  11489232281, 1786190,
  8 | 114, 199633,  57, 2181162, 17632,  998165, 33573,  38126842081, 2283762,
  9 | 115, 460759,  92, 5122307, 67735, 7372144, 89355, 204995005981, 3311655,
etc.
		

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A246278, A341605, A341606, A341526.

Cf. A341627 (denominators).

Programs

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));
A341626sq(row,col) = A341526(A246278sq(row,col));
A341626list(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] = A341626sq(col,(a-(col-1))))); (v); };
v341626 = A341626list(up_to);
A341626(n) = v341626[n];

Formula

A(n,k) = A341526(A246278(n,k)).

If we set r(row,col) = A341605(row,col)/A341606(row,col) and d(row,col) = A(row,col)/A341627(row,col), then d(row,col) = r(row+1,col)/r(row,col).

For all n, k, A(n,k) < A341627(n, k).