A328631 Square array where the row n lists all nonnegative numbers k for which A328578(k) = n, read by falling antidiagonals.

1, 3, 0, 5, 12, 2, 7, 24, 6, 4, 9, 30, 18, 8, 10, 11, 42, 34, 16, 14, 20, 13, 54, 36, 32, 38, 22, 28, 15, 60, 48, 64, 58, 26, 50, 82, 17, 72, 66, 152, 62, 40, 52, 88, 116, 19, 84, 78, 184, 112, 44, 56, 106, 118, 148, 21, 90, 96, 210, 166, 46, 74, 110, 140, 178, 208, 23, 102, 108, 242, 176, 68, 76, 128, 142, 196, 412, 418

Offset: 1

Author

Antti Karttunen, Oct 27 2019

Keywords

• nonn
• tabl

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 A328578(x) = n.

Examples

			The top left 12 X 12 corner of the array:
   n +------------------------------------------------------
   1 |   1,   3,   5,   7,   9,  11,  13,  15,  17,  19, ...
   2 |   0,  12,  24,  30,  42,  54,  60,  72,  84,  90, ...
   3 |   2,   6,  18,  34,  36,  48,  66,  78,  96, 108, ...
   4 |   4,   8,  16,  32,  64, 152, 184, 210, 242, 274, ...
   5 |  10,  14,  38,  58,  62, 112, 166, 176, 214, 218, ...
   6 |  20,  22,  26,  40,  44,  46,  68,  70,  86,  92, ...
   7 |  28,  50,  52,  56,  74,  76,  80,  94,  98, 100, ...
   8 |  82,  88, 106, 110, 128, 130, 134, 158, 182, 262, ...
   9 | 116, 118, 140, 142, 146, 160, 164, 170, 188, 190, ...
  10 | 148, 178, 196, 200, 202, 206, 328, 352, 374, 376, ...
  11 | 208, 412, 416, 562, 568, 586, 590, 592, 596, 614, ...
  12 | 418, 598, 626, 628, 778, 800, 802, 826, 830, 832, ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1081; the first 46 antidiagonals of the array
• Index entries for sequences that are permutations of the natural numbers
• Index entries for sequences related to primorial base

Crossrefs

Rows 1-6: A005408, A328632, A328633, A328634, A328635, A328636.

Column 1: A328761.

Cf. A257993, A276086, A328578.

Programs

PARI

up_to = 78;
A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328578(n) = A257993(A276086(A276086(n)));
memoA328631sq = Map();
A328631sq(n, k) = { my(v=0); if(!mapisdefined(memoA328631sq,[n,k-1],&v),if(1==k, v=-1, v = A328631sq(n, k-1))); for(i=1+v,oo,if(A328578(i)==n,mapput(memoA328631sq,[n,k],i); return(i))); };
A328631list(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] = A328631sq(col,(a-(col-1))))); (v); };
v328631 = A328631list(up_to);
A328631(n) = v328631[n];