A354940 - OEIS

A354940

Square array A(n, k) = A354930(n, k)/n, read by falling antidiagonals.

%I #8 Jun 16 2022 10:26:29

%S 1,2,3,3,5,4,4,7,7,5,5,9,13,9,3,7,11,16,13,6,7,8,13,19,17,8,13,4,9,17,

%T 25,21,11,19,5,3,11,19,31,25,13,25,8,9,5,13,23,37,29,16,31,11,11,7,11,

%U 16,25,43,37,23,37,15,17,10,31,3,17,27,49,41,26,43,19,19,14,41,4,13,19,29,61,49,31,49,22,25,16,51,6,25,7

%N Square array A(n, k) = A354930(n, 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), etc.

%e The top left 15x16 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 | 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41,

%e 3 | 4, 7, 13, 16, 19, 25, 31, 37, 43, 49, 61, 64, 67, 73, 79,

%e 4 | 5, 9, 13, 17, 21, 25, 29, 37, 41, 49, 53, 57, 61, 73, 81,

%e 5 | 3, 6, 8, 11, 13, 16, 23, 26, 31, 36, 41, 43, 46, 51, 53,

%e 6 | 7, 13, 19, 25, 31, 37, 43, 49, 61, 67, 73, 79, 97, 103, 109,

%e 7 | 4, 5, 8, 11, 15, 19, 22, 25, 29, 32, 39, 43, 47, 50, 53,

%e 8 | 3, 9, 11, 17, 19, 25, 27, 33, 41, 43, 49, 57, 59, 67, 73,

%e 9 | 5, 7, 10, 14, 16, 19, 23, 25, 28, 32, 37, 41, 43, 46, 50,

%e 10 | 11, 31, 41, 51, 61, 71, 81, 91, 101, 121, 131, 141, 151, 171, 181,

%e 11 | 3, 4, 6, 9, 12, 15, 17, 23, 25, 28, 31, 34, 37, 45, 47,

%e 12 | 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 145, 157, 169, 181, 193,

%e 13 | 7, 8, 9, 11, 14, 20, 22, 23, 27, 33, 37, 40, 46, 47, 48,

%e 14 | 5, 15, 19, 29, 43, 47, 57, 61, 71, 89, 99, 103, 113, 127, 131,

%e 15 | 4, 8, 16, 19, 23, 31, 38, 46, 49, 53, 61, 64, 76, 79, 83,

%e 16 | 7, 11, 13, 17, 23, 27, 29, 33, 43, 49, 59, 61, 65, 71, 75,

%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 A354940sq(n, k) = (A354930sq(n, k)/n);

%o A354940list(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] = A354940sq(col,(a-(col-1))))); (v); };

%o v354940 = A354940list(up_to);

%o A354940(n) = v354940[n];

%Y Cf. A345992, A354930.

%Y Cf. A354932 (column 1).

%Y Rows 1 .. 7 (some of these are conjectural): A000961, A061345 (without its initial 1), A137827, A354934, A354935, A354936, A354937, A354938, A354939.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, Jun 15 2022