A354930 Square array where the row n lists all nonnegative numbers k for which A345992(k) = n, read by falling antidiagonals.

1, 2, 6, 3, 10, 12, 4, 14, 21, 20, 5, 18, 39, 36, 15, 7, 22, 48, 52, 30, 42, 8, 26, 57, 68, 40, 78, 28, 9, 34, 75, 84, 55, 114, 35, 24, 11, 38, 93, 100, 65, 150, 56, 72, 45, 13, 46, 111, 116, 80, 186, 77, 88, 63, 110, 16, 50, 129, 148, 115, 222, 105, 136, 90, 310, 33, 17, 54, 147, 164, 130, 258, 133, 152, 126, 410, 44, 156

Offset

1,2

Comments

Array is read by descending antidiagonals with (n,k) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ... where A(n,k) is the k-th solution x to A345992(x) = n.

Links

Table of n, a(n) for n=1..78.

Index entries for sequences that are permutations of the natural numbers

Example

The top left 15x9 corner of the array:
n\k |  1   2    3    4    5    6    7    8    9   10   11   12   13   14   15
----+--------------------------------------------------------------------------
  1 |  1,  2,   3,   4,   5,   7,   8,   9,  11,  13,  16,  17,  19,  23,  25,
  2 |  6, 10,  14,  18,  22,  26,  34,  38,  46,  50,  54,  58,  62,  74,  82,
  3 | 12, 21,  39,  48,  57,  75,  93, 111, 129, 147, 183, 192, 201, 219, 237,
  4 | 20, 36,  52,  68,  84, 100, 116, 148, 164, 196, 212, 228, 244, 292, 324,
  5 | 15, 30,  40,  55,  65,  80, 115, 130, 155, 180, 205, 215, 230, 255, 265,
  6 | 42, 78, 114, 150, 186, 222, 258, 294, 366, 402, 438, 474, 582, 618, 654,
  7 | 28, 35,  56,  77, 105, 133, 154, 175, 203, 224, 273, 301, 329, 350, 371,
  8 | 24, 72,  88, 136, 152, 200, 216, 264, 328, 344, 392, 456, 472, 536, 584,
  9 | 45, 63,  90, 126, 144, 171, 207, 225, 252, 288, 333, 369, 387, 414, 450,

Prog

(PARI)
up_to = 105;
A345992(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n, m))));
memoA354930sq = Map();
A354930sq(n, k) = { my(v=0); if(!mapisdefined(memoA354930sq, [n, k-1], &v), if(1==k, v=0, v = A354930sq(n, k-1))); for(i=1+v, oo, if(A345992(i)==n, mapput(memoA354930sq, [n, k], i); return(i))); };
A354930list(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] = A354930sq(col, (a-(col-1))))); (v); };
v354930 = A354930list(up_to);
A354930(n) = v354930[n];

Crossrefs

Cf. A344005, A345992.

Column 1: A354931.

Rows 1..3: A000961, A278568 (without its initial 2, conjectured), A354984 (conjectured).

See also array A354940 where the entries are divided by their row index.

Sequence in context: A365810 A375281 A167979 * A276578 A277810 A180428

Adjacent sequences: A354927 A354928 A354929 * A354931 A354932 A354933

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 14 2022

Status

approved