A354940 Square array A(n, k) = A354930(n, k)/n, read by falling antidiagonals.

1, 2, 3, 3, 5, 4, 4, 7, 7, 5, 5, 9, 13, 9, 3, 7, 11, 16, 13, 6, 7, 8, 13, 19, 17, 8, 13, 4, 9, 17, 25, 21, 11, 19, 5, 3, 11, 19, 31, 25, 13, 25, 8, 9, 5, 13, 23, 37, 29, 16, 31, 11, 11, 7, 11, 16, 25, 43, 37, 23, 37, 15, 17, 10, 31, 3, 17, 27, 49, 41, 26, 43, 19, 19, 14, 41, 4, 13, 19, 29, 61, 49, 31, 49, 22, 25, 16, 51, 6, 25, 7

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), etc.

Links

Table of n, a(n) for n=1..91.

Example

The top left 15x16 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 |  3,  5,  7,  9, 11, 13, 17, 19,  23,  25,  27,  29,  31,  37,  41,
   3 |  4,  7, 13, 16, 19, 25, 31, 37,  43,  49,  61,  64,  67,  73,  79,
   4 |  5,  9, 13, 17, 21, 25, 29, 37,  41,  49,  53,  57,  61,  73,  81,
   5 |  3,  6,  8, 11, 13, 16, 23, 26,  31,  36,  41,  43,  46,  51,  53,
   6 |  7, 13, 19, 25, 31, 37, 43, 49,  61,  67,  73,  79,  97, 103, 109,
   7 |  4,  5,  8, 11, 15, 19, 22, 25,  29,  32,  39,  43,  47,  50,  53,
   8 |  3,  9, 11, 17, 19, 25, 27, 33,  41,  43,  49,  57,  59,  67,  73,
   9 |  5,  7, 10, 14, 16, 19, 23, 25,  28,  32,  37,  41,  43,  46,  50,
  10 | 11, 31, 41, 51, 61, 71, 81, 91, 101, 121, 131, 141, 151, 171, 181,
  11 |  3,  4,  6,  9, 12, 15, 17, 23,  25,  28,  31,  34,  37,  45,  47,
  12 | 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 145, 157, 169, 181, 193,
  13 |  7,  8,  9, 11, 14, 20, 22, 23,  27,  33,  37,  40,  46,  47,  48,
  14 |  5, 15, 19, 29, 43, 47, 57, 61,  71,  89,  99, 103, 113, 127, 131,
  15 |  4,  8, 16, 19, 23, 31, 38, 46,  49,  53,  61,  64,  76,  79,  83,
  16 |  7, 11, 13, 17, 23, 27, 29, 33,  43,  49,  59,  61,  65,  71,  75,

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))); };
A354940sq(n, k) = (A354930sq(n, k)/n);
A354940list(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] = A354940sq(col, (a-(col-1))))); (v); };
v354940 = A354940list(up_to);
A354940(n) = v354940[n];

Crossrefs

Cf. A345992, A354930.

Cf. A354932 (column 1).

Rows 1 .. 7 (some of these are conjectural): A000961, A061345 (without its initial 1), A137827, A354934, A354935, A354936, A354937, A354938, A354939.

Sequence in context: A375465 A257004 A126571 * A210874 A244796 A080391

Adjacent sequences: A354937 A354938 A354939 * A354941 A354942 A354943

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 15 2022

Status

approved