A389169 Square array A(n,k) = A388979(A388981(n, k)), read by descending antidiagonals.

520, 1368, 4704, 952, 11040, 34848, 1848, 8976, 77280, 209040, 3016, 14352, 53664, 388080, 788256, 29200, 21216, 78336, 301920, 1220544, 2210688, 5904, 1380288, 105792, 401280, 1021440, 3231360, 5216400, 4488, 46800, 49262400, 524400, 1321488, 2848320, 7062528, 12525216, 6232, 29184, 221088, 1368400800, 1880592, 4025664, 7287120, 19126800, 31768800

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals of the array

Ratio A389169(n)/A389168(n) plotted with OEIS Plot tool

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Formula

A(n, k) > A389168(n, k).

Example

The top left corner of the array:
k= |        1         2         3         4         5              6         7
---+---------------------------------------------------------------------------
1  |      520,     1368,      952,     1848,     3016,         29200,     5904,
2  |     4704,    11040,     8976,    14352,    21216,       1380288,    46800,
3  |    34848,    77280,    53664,    78336,   105792,      49262400,   221088,
4  |   209040,   388080,   301920,   401280,   524400,    1368400800,   868032,
5  |   788256,  1220544,  1021440,  1321488,  1880592,   17053404480,  2311920,
6  |  2210688,  3231360,  2848320,  4025664,  4999680,  113277841920,  5636928,
7  |  5216400,  7062528,  7287120,  8928000, 11108880,  563209938720, 15066240,
8  | 12525216, 19126800, 15254976, 18949920, 23466432, 2467540130880, 31397760,

Prog

(PARI)
up_to_cols = 210;
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A388984list(up_to) = { my(v=vector(up_to), i=0); forstep(n=2, oo, 2, if(isprime(core(n)) && !isprimepower(n), i++; v[i] = n; if(i==up_to, return(v)))); };
v388984 = A388984list(up_to_cols);
A388984(n) = v388984[n];
up_to = binomial(up_to_cols+1, 2)
A388981sq(row, col) = if(1==row, A388984(col), my(f = factor(A388984(col))); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));
A388979(n) = ((sigma(n)-core(n)-n)*(A003961(n)-A003961(core(n))));
A389169sq(row, col) = A388979(A388981sq(row, col));
A389169list(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] = A389169sq(col, (a-(col-1))))); (v); };
v389169 = A389169list(up_to);
A389169(n) = v389169[n];

Crossrefs

Cf. A388979, A388981, A389168.

Cf. also A388987, A388988, A388993 and A341529/A341528.

Sequence in context: A235274 A147854 A147856 * A388279 A094903 A250693

Adjacent sequences: A389166 A389167 A389168 * A389170 A389171 A389172

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 25 2025

Status

approved