A389168 Square array A(n,k) = A388978(A388981(n, k)), read by descending antidiagonals.

252, 736, 2640, 510, 6624, 22512, 966, 4816, 50400, 145728, 1716, 8448, 39072, 273840, 630240, 14220, 12064, 54912, 199680, 975744, 1799280, 3744, 746400, 77520, 279072, 877200, 2635776, 4476096, 2496, 27072, 31405920, 352032, 1098960, 2228016, 6058800, 10101600, 3570, 17136, 164400, 927273600, 1545600, 3091200, 6173568, 15429216, 27102240

Offset

1,1

Links

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

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Formula

A(n, k) < A389169(n, k).

Example

The top left corner of the array:
k= |        1         2         3         4         5              6         7
----+--------------------------------------------------------------------------
1  |      252,      736,      510,      966,     1716,         14220,     3744,
2  |     2640,     6624,     4816,     8448,    12064,        746400,    27072,
3  |    22512,    50400,    39072,    54912,    77520,      31405920,   164400,
4  |   145728,   273840,   199680,   279072,   352032,     927273600,   580944,
5  |   630240,   975744,   877200,  1098960,  1545600,   13585802880,  1989504,
6  |  1799280,  2635776,  2228016,  3091200,  4063248,   91230179040,  4417920,
7  |  4476096,  6058800,  6173568,  8101440,  9677952,  482503559040, 12763872,
8  | 10101600, 15429216, 13217040, 15668640, 19926720, 1982489872320, 27227760,

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));
A388978(n) = { my(u=A003961(n)); ((n-core(n))*(sigma(u)-core(u)-u)); };
A389168sq(row, col) = A388978(A388981sq(row, col));
A389168list(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] = A389168sq(col, (a-(col-1))))); (v); };
v389168 = A389168list(up_to);
A389168(n) = v389168[n];

Crossrefs

Cf. A388978, A388981, A389169.

Cf. also A388987, A388988, A388993.

Sequence in context: A254467 A242570 A046379 * A250794 A245858 A200884

Adjacent sequences: A389165 A389166 A389167 * A389169 A389170 A389171

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 25 2025

Status

approved