A388285 Square array A(n, k) = 3*A246278(n, k) - sigma(A246278(n, k)), read by falling antidiagonals. A033885(n) = 3*n-sigma(n) as applied to the prime shift array.

3, 5, 5, 6, 14, 9, 9, 21, 44, 13, 12, 41, 57, 90, 21, 8, 31, 219, 135, 230, 25, 18, 57, 93, 629, 261, 324, 33, 17, 51, 277, 161, 2529, 411, 560, 37, 15, 122, 111, 933, 345, 4211, 609, 702, 45, 18, 101, 1094, 213, 2857, 461, 9519, 831, 1034, 57, 30, 85, 393, 4402, 387, 5325, 741, 13337, 1281, 1652, 61

Offset

1,1

Links

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

Index entries for sequences computed from indices in prime factorization.

Index entries for sequences related to sigma(n).

Formula

A(n, k) = A033885(A246278(n, k)) = 3*A246278(n, k) - A355927(n, k).

A(n, k) = A246278(n,k) + A378979(n, k).

A(n, k) = A388284(n,k) * A355925(n, k).

Example

The top left corner of the array:
k=  |  1    2    3     4    5      6    7       8      9     10    11      12
2k= |  2    4    6     8   10     12   14      16     18     20    22      24
----+-------------------------------------------------------------------------
1   |  3,   5,   6,    9,  12,     8,  18,     17,    15,    18,   30,     12,
2   |  5,  14,  21,   41,  31,    57,  51,    122,   101,    85,   61,    165,
3   |  9,  44,  57,  219,  93,   277, 111,   1094,   393,   453,  147,   1377,
4   | 13,  90, 135,  629, 161,   933, 213,   4402,  1477,  1113,  239,   6519,
5   | 21, 230, 261, 2529, 345,  2857, 387,  27818,  3381,  3777,  471,  31413,
6   | 25, 324, 411, 4211, 461,  5325, 561,  54742,  6973,  5973,  711,  69207,
7   | 33, 560, 609, 9519, 741, 10333, 939, 161822, 11553, 12573, 1005, 175641,
Columns 60 and 90:
k=  |       60                90
2k= |      120               180
----+------------------------------
1   |        0,               -6,
2   |      915,             1501,
3   |    13899,            19221,
4   |    79947,           125097,
5   |   513525,           604797,
6   |  1272093,          1660317,
7   |  3935343,          4391493,
8   |  8512059,         10293513,
9   | 20603199,         25961461,

Prog

(PARI)
up_to = 66;
A033885(n) = (3*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));
A388285sq(row, col) = A033885(A246278sq(row, col));
A388285list(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] = A388285sq(col, (a-(col-1))))); (v); };
v388285 = A388285list(up_to);
A388285(n) = v388285[n];

Crossrefs

Cf. A033885, A246278, A355925, A355927, A378979, A388284.

Sequence in context: A055594 A276173 A197631 * A266567 A282624 A179858

Adjacent sequences: A388282 A388283 A388284 * A388286 A388287 A388288

Keyword

sign,tabl

Author

Antti Karttunen, Sep 21 2025

Status

approved