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%I #11 Jun 15 2022 14:36:25
%S 1,2,6,3,10,12,4,14,21,20,5,18,39,36,15,7,22,48,52,30,42,8,26,57,68,
%T 40,78,28,9,34,75,84,55,114,35,24,11,38,93,100,65,150,56,72,45,13,46,
%U 111,116,80,186,77,88,63,110,16,50,129,148,115,222,105,136,90,310,33,17,54,147,164,130,258,133,152,126,410,44,156
%N Square array where the row n lists all nonnegative numbers k for which A345992(k) = n, read by falling antidiagonals.
%C 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 A345992(x) = n.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The top left 15x9 corner of the array:
%e n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e ----+--------------------------------------------------------------------------
%e 1 | 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25,
%e 2 | 6, 10, 14, 18, 22, 26, 34, 38, 46, 50, 54, 58, 62, 74, 82,
%e 3 | 12, 21, 39, 48, 57, 75, 93, 111, 129, 147, 183, 192, 201, 219, 237,
%e 4 | 20, 36, 52, 68, 84, 100, 116, 148, 164, 196, 212, 228, 244, 292, 324,
%e 5 | 15, 30, 40, 55, 65, 80, 115, 130, 155, 180, 205, 215, 230, 255, 265,
%e 6 | 42, 78, 114, 150, 186, 222, 258, 294, 366, 402, 438, 474, 582, 618, 654,
%e 7 | 28, 35, 56, 77, 105, 133, 154, 175, 203, 224, 273, 301, 329, 350, 371,
%e 8 | 24, 72, 88, 136, 152, 200, 216, 264, 328, 344, 392, 456, 472, 536, 584,
%e 9 | 45, 63, 90, 126, 144, 171, 207, 225, 252, 288, 333, 369, 387, 414, 450,
%o (PARI)
%o up_to = 105;
%o A345992(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n,m))));
%o memoA354930sq = Map();
%o 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))); };
%o A354930list(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] = A354930sq(col,(a-(col-1))))); (v); };
%o v354930 = A354930list(up_to);
%o A354930(n) = v354930[n];
%Y Cf. A344005, A345992.
%Y Column 1: A354931.
%Y Rows 1..3: A000961, A278568 (without its initial 2, conjectured), A354984 (conjectured).
%Y See also array A354940 where the entries are divided by their row index.
%K nonn,tabl
%O 1,2
%A _Antti Karttunen_, Jun 14 2022
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