A388284 Square array A(n, k) = A388283(A246278(n, k)), read by falling antidiagonals. Numerator of (3*n-sigma(n))/n, as applied to the prime shift array.

3, 5, 5, 1, 14, 9, 9, 7, 44, 13, 6, 41, 57, 90, 21, 2, 31, 219, 135, 230, 25, 9, 19, 93, 629, 261, 324, 33, 17, 17, 277, 23, 2529, 411, 560, 37, 5, 122, 111, 933, 345, 4211, 609, 702, 45, 9, 101, 1094, 213, 2857, 461, 9519, 831, 1034, 57, 15, 85, 393, 4402, 387, 5325, 741, 13337, 1281, 1652, 61, 1, 61, 453, 211, 27818, 561, 10333, 1053, 23781, 1737, 1890, 73

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) = A388283(A246278(n, k)).

A(n, k) = A388285(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,    1,     9,    6,     2,    9,     17,     5,     9,   15,      1,
  2   |  5,   14,    7,    41,   31,    19,   17,    122,   101,    85,   61,     11,
  3   |  9,   44,   57,   219,   93,   277,  111,   1094,   393,   453,  147,   1377,
  4   | 13,   90,  135,   629,   23,   933,  213,   4402,   211,   159,  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,   4071,
  7   | 33,  560,  609,  9519,  741, 10333,  939, 161822, 11553, 12573, 1005, 175641,
  8   | 37,  702,  831, 13337, 1053, 15765, 1127, 253402, 19093, 19977,   71, 299511,
  9   | 45, 1034, 1281, 23781, 1371, 29433, 1641, 546962, 37125, 31501, 1821, 676929,
Columns 60 and 90:
  k=  |       60                90
  2k= |      120               180
  ----+------------------------------
  1   |        0,               -1,
  2   |       61,             1501,
  3   |    13899,            19221,
  4   |    11421,             2553,
  5   |   513525,           604797,
  6   |    74829,          1660317,
  7   |  3935343,          4391493,
  8   |  8512059,         10293513,
  9   | 20603199,         25961461,

Prog

(PARI)
up_to = 78;
A388283(n) = numerator((3*n - sigma(n))/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));
A388284sq(row, col) = A388283(A246278sq(row, col));
A388284list(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] = A388284sq(col, (a-(col-1))))); (v); };
v388284 = A388284list(up_to);
A388284(n) = v388284[n];

Crossrefs

Cf. A246278, A341606 (denominators), A355927, A388283, A388285.

Cf. also A341605.

Sequence in context: A388880 A077860 A261340 * A387987 A078063 A373304

Adjacent sequences: A388281 A388282 A388283 * A388285 A388286 A388287

Keyword

sign,frac,tabl

Author

Antti Karttunen, Sep 21 2025

Status

approved