A351962 Square array A(n,k) = A156552(lcm(A005940(1+n), A005940(1+k))), read by antidiagonals.

0, 1, 1, 2, 1, 2, 3, 5, 5, 3, 4, 3, 2, 3, 4, 5, 9, 11, 11, 9, 5, 6, 5, 10, 3, 10, 5, 6, 7, 13, 5, 19, 19, 5, 13, 7, 8, 7, 6, 11, 4, 11, 6, 7, 8, 9, 17, 23, 27, 21, 21, 27, 23, 17, 9, 10, 9, 18, 7, 22, 5, 22, 7, 18, 9, 10, 11, 21, 21, 35, 39, 13, 13, 39, 35, 21, 21, 11, 12, 11, 10, 19, 20, 23, 6, 23, 20, 19, 10, 11, 12

Offset

0,4

Comments

The indices run as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), etc. The array is symmetric.

Links

Table of n, a(n) for n=0..90.

Index entries for sequences related to binary expansion of n

Index entries for sequences related to lcm's

Example

The top left corner of the array:
      n=0   1   2   3   4   5    6    7    8   9   10   11   12
-----|-----------------------------------------------------------
k= 0 |  0,  1,  2,  3,  4,  5,   6,   7,   8,  9,  10,  11,  12,
   1 |  1,  1,  5,  3,  9,  5,  13,   7,  17,  9,  21,  11,  25,
   2 |  2,  5,  2, 11, 10,  5,   6,  23,  18, 21,  10,  11,  26,
   3 |  3,  3, 11,  3, 19, 11,  27,   7,  35, 19,  43,  11,  51,
   4 |  4,  9, 10, 19,  4, 21,  22,  39,  20,  9,  10,  43,  12,
   5 |  5,  5,  5, 11, 21,  5,  13,  23,  37, 21,  21,  11,  53,
   6 |  6, 13,  6, 27, 22, 13,   6,  55,  38, 45,  22,  27,  54,
   7 |  7,  7, 23,  7, 39, 23,  55,   7,  71, 39,  87,  23, 103,
   8 |  8, 17, 18, 35, 20, 37,  38,  71,   8, 41,  42,  75,  44,
   9 |  9,  9, 21, 19,  9, 21,  45,  39,  41,  9,  21,  43,  25,
  10 | 10, 21, 10, 43, 10, 21,  22,  87,  42, 21,  10,  43,  26,
  11 | 11, 11, 11, 11, 43, 11,  27,  23,  75, 43,  43,  11, 107,
  12 | 12, 25, 26, 51, 12, 53,  54, 103,  44, 25,  26, 107,  12,
  13 | 13, 13, 13, 27, 45, 13,  13,  55,  77, 45,  45,  27, 109,
  14 | 14, 29, 14, 59, 46, 29,  14, 119,  78, 93,  46,  59, 110,
  15 | 15, 15, 47, 15, 79, 47, 111,  15, 143, 79, 175,  47, 207,
  16 | 16, 33, 34, 67, 36, 69,  70, 135,  40, 73,  74, 139,  76,

Prog

(PARI)
up_to = 104;
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A351962sq(n, k) = A156552(lcm(A005940(1+n), A005940(1+k)));
A351962list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(col=0, a, i++; if(i > #v, return(v)); v[i] = A351962sq(col, (a-(col))))); (v); };
v351962 = A351962list(up_to);
A351962(n) = v351962[1+n];

Crossrefs

Cf. A003990, A005940, A156552.

Cf. A001477 (main diagonal).

Cf. also A341520, A351960, A351961.

Sequence in context: A363226 A075758 A125596 * A253026 A341145 A204994

Adjacent sequences: A351959 A351960 A351961 * A351963 A351964 A351965

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 26 2022

Status

approved