A379499 Square array A(n, k) = A064987(A246278(n, k)), read by falling antidiagonals; A064987(n) = n*sigma(n), applied to the prime shift array.

6, 28, 12, 72, 117, 30, 120, 360, 775, 56, 180, 1080, 1680, 2793, 132, 336, 672, 19500, 7392, 16093, 182, 336, 3510, 3960, 137200, 24024, 30927, 306, 496, 1584, 43400, 10192, 1948584, 55692, 88723, 380, 702, 9801, 5460, 368676, 40392, 5228860, 116280, 137541, 552, 840, 9300, 488125, 17136, 2928926, 69160, 25645860, 209760, 292537, 870

Offset: 1

Author

Antti Karttunen, Jan 02 2025

Keywords

• nonn
• tabl

Comments

Each column is strictly monotonic.

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,    72,     120,   180,     336,   336,       496,     702,     840,
2 |  12,   117,   360,    1080,   672,    3510,  1584,      9801,    9300,    6552,
3 |  30,   775,  1680,   19500,  3960,   43400,  5460,    488125,   83790,  102300,
4 |  56,  2793,  7392,  137200, 10192,  368676, 17136,   6725201,  901208,  508326,
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 A246278 and A355927.

Cf. A000203, A003961, A064987, A379500.

Programs

PARI

up_to = 55;
A064987(n) = (n*sigma(n));
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));
A379499sq(row,col) = A064987(A246278sq(row,col));
A379499list(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] = A379499sq(col,(a-(col-1))))); (v); };
v379499 = A379499list(up_to);
A379499(n) = v379499[n];

Formula

A(n, k) = A246278(n, k) * A355927(n, k).