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A335910
Square array where row n lists all numbers k for which A335885(k) = n, read by falling antidiagonals.
5
1, 2, 3, 4, 5, 9, 8, 6, 11, 27, 16, 7, 13, 33, 81, 32, 10, 15, 37, 99, 243, 64, 12, 18, 39, 107, 297, 729, 128, 14, 19, 43, 109, 321, 891, 2187, 256, 17, 21, 45, 111, 327, 963, 2673, 6561, 512, 20, 22, 53, 117, 333, 981, 2889, 8019, 19683, 1024, 24, 23, 54, 121, 351, 999, 2943, 8667, 24057, 59049, 2048, 28, 25, 55, 129, 363, 1053, 2997, 8829, 26001, 72171, 177147
OFFSET
0,2
COMMENTS
Array is read by descending antidiagonals with (n,k) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), ... where A(n,k) is the (k+1)-th solution x to A335885(x) = n. The row indexing (n) starts from 0, and column indexing (k) also from 0.
For any odd prime p that appears on row n, either p-1 or p+1 appears on row n-1.
The e-th powers of the terms on row n form a subset of terms on row (e*n). More generally, a product of terms that occur on rows i_1, i_2, ..., i_k can be found at row (i_1 + i_2 + ... + i_k), because A335885 is completely additive.
EXAMPLE
The top left corner of the array:
n\k | 0 1 2 3 4 5 6 7 8 9
----+--------------------------------------------------------------------------
0 | 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...
1 | 3, 5, 6, 7, 10, 12, 14, 17, 20, 24, ...
2 | 9, 11, 13, 15, 18, 19, 21, 22, 23, 25, ...
3 | 27, 33, 37, 39, 43, 45, 53, 54, 55, 57, ...
4 | 81, 99, 107, 109, 111, 117, 121, 129, 131, 135, ...
5 | 243, 297, 321, 327, 333, 351, 363, 387, 393, 405, ...
6 | 729, 891, 963, 981, 999, 1053, 1089, 1161, 1177, 1179, ...
7 | 2187, 2673, 2889, 2943, 2997, 3159, 3267, 3483, 3531, 3537, ...
8 | 6561, 8019, 8667, 8829, 8991, 9477, 9801, 10449, 10593, 10611, ...
9 | 19683, 24057, 26001, 26487, 26973, 28431, 29403, 31347, 31779, 31833, ...
PROG
(PARI)
up_to = 78-1; \\ = binomial(12+1, 2)-1.
memoA335885 = Map();
A335885(n) = if(1==n, 0, my(v=0); if(mapisdefined(memoA335885, n, &v), v, my(f=factor(n)); v = sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+min(A335885(f[k, 1]-1), A335885(f[k, 1]+1))))); mapput(memoA335885, n, v); (v)));
memoA335910sq = Map();
A335910sq(n, k) = { my(v=0); if((0==k), v = -1, if(!mapisdefined(memoA335910sq, [n, k-1], &v), v = A335910sq(n, k-1))); for(i=1+v, oo, if(A335885(1+i)==n, mapput(memoA335910sq, [n, k], i); return(1+i))); };
A335910list(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] = A335910sq(col, (a-(col))))); (v); };
v335910 = A335910list(up_to);
A335910(n) = v335910[1+n];
for(n=0, up_to, print1(A335910(n), ", "));
CROSSREFS
Cf. A335885.
Cf. A000079, A335911, A335912 (rows 0-2), A000244 (is very like the leftmost column).
Cf. also arrays A334100, A335430.
Sequence in context: A164340 A046021 A319023 * A362814 A371152 A266531
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Jul 01 2020
STATUS
approved