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

1,1

Comments

Each column is strictly monotonic.

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)

Formula

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

Example

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,

Prog

(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];

Crossrefs

Elementwise product of arrays A246278 and A355927.

Cf. A000203, A003961, A064987, A379500.

Sequence in context: A211679 A379500 A261868 * A342922 A357462 A105402

Adjacent sequences: A379496 A379497 A379498 * A379500 A379501 A379502

Keyword

nonn,tabl,new

Author

Antti Karttunen, Jan 02 2025

Status

approved