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

1,1

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

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

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,     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,

Prog

(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];

Crossrefs

Elementwise product of arrays A341605 and A341606.

Cf. A246278, A249670, A355925, A379499.

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

Sequence in context: A091911 A215896 A211679 * A261868 A379499 A342922

Adjacent sequences: A379497 A379498 A379499 * A379501 A379502 A379503

Keyword

nonn,tabl

Author

Antti Karttunen, Jan 02 2025

Status

approved