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A328631
Square array where the row n lists all nonnegative numbers k for which A328578(k) = n, read by falling antidiagonals.
8
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
1,2
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 A328578(x) = n.
EXAMPLE
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, ...
PROG
(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); };
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];
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Oct 27 2019
STATUS
approved