A379500 Square array A(n, k) = A249670(A246278(n, k)), read by falling antidiagonals; A249670(n) = A017665(n)*A017666(n), applied to the prime shift array.

6, 28, 12, 2, 117, 30, 120, 40, 775, 56, 45, 1080, 1680, 2793, 132, 21, 672, 19500, 7392, 16093, 182, 84, 390, 3960, 137200, 24024, 30927, 306, 496, 176, 43400, 208, 1948584, 55692, 88723, 380, 78, 9801, 5460, 368676, 40392, 5228860, 116280, 137541, 552, 210, 9300, 488125, 17136, 2928926, 69160, 25645860, 209760, 292537, 870

Offset: 1

Author

Antti Karttunen, Jan 02 2025

Keywords

• nonn
• tabl

Examples

			The top left corner of the array:
k=|   1      2      3        4      5        6      7          8        9       10
2k|   2      4      6        8     10       12     14         16       18       20
--+---------------------------------------------------------------------------------
1 |   6,    28,     2,     120,    45,      21,    84,       496,      78,     210,
2 |  12,   117,    40,    1080,   672,     390,   176,      9801,    9300,    6552,
3 |  30,   775,  1680,   19500,  3960,   43400,  5460,    488125,   83790,  102300,
4 |  56,  2793,  7392,  137200,   208,  368676, 17136,   6725201,   18392,   10374,
5 | 132, 16093, 24024, 1948584, 40392, 2928926, 50160, 235793305, 4082364, 4924458,
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11325; the first 150 antidiagonals of array
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Elementwise product of arrays A341605 and A341606.

Cf. A246278, A249670, A355925, A379499.

Cf. A036690 (leftmost column), A361468 (even bisection gives row 2).

Programs

PARI

up_to = 55;
A249670(n) = { my(ab = sigma(n)/n); numerator(ab)*denominator(ab); };
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));
A379500sq(row,col) = A249670(A246278sq(row,col));
A379500list(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] = A379500sq(col,(a-(col-1))))); (v); };
v379500 = A379500list(up_to);
A379500(n) = v379500[n];

Formula

A(n, k) = A341605(n, k) * A341606(n, k).

A(n, k) = A379499(n, k) / (A355925(n, k)^2).