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A354930 Square array where the row n lists all nonnegative numbers k for which A345992(k) = n, read by falling antidiagonals. 5
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, 40, 78, 28, 9, 34, 75, 84, 55, 114, 35, 24, 11, 38, 93, 100, 65, 150, 56, 72, 45, 13, 46, 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 (list; table; graph; refs; listen; history; text; internal format)
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 A345992(x) = n.

LINKS

Table of n, a(n) for n=1..78.

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

The top left 15x9 corner of the array:

n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

----+--------------------------------------------------------------------------

1 | 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25,

2 | 6, 10, 14, 18, 22, 26, 34, 38, 46, 50, 54, 58, 62, 74, 82,

3 | 12, 21, 39, 48, 57, 75, 93, 111, 129, 147, 183, 192, 201, 219, 237,

4 | 20, 36, 52, 68, 84, 100, 116, 148, 164, 196, 212, 228, 244, 292, 324,

5 | 15, 30, 40, 55, 65, 80, 115, 130, 155, 180, 205, 215, 230, 255, 265,

6 | 42, 78, 114, 150, 186, 222, 258, 294, 366, 402, 438, 474, 582, 618, 654,

7 | 28, 35, 56, 77, 105, 133, 154, 175, 203, 224, 273, 301, 329, 350, 371,

8 | 24, 72, 88, 136, 152, 200, 216, 264, 328, 344, 392, 456, 472, 536, 584,

9 | 45, 63, 90, 126, 144, 171, 207, 225, 252, 288, 333, 369, 387, 414, 450,

PROG

(PARI)

up_to = 105;

A345992(n) = for(m=1, oo, if((m*(m+1))%n==0, return(gcd(n, m))));

memoA354930sq = Map();

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))); };

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); };

v354930 = A354930list(up_to);

A354930(n) = v354930[n];

CROSSREFS

Cf. A344005, A345992.

Column 1: A354931.

Rows 1..3: A000961, A278568 (without its initial 2, conjectured), A354984 (conjectured).

See also array A354940 where the entries are divided by their row index.

Sequence in context: A090705 A208547 A167979 * A276578 A277810 A180428

Adjacent sequences: A354927 A354928 A354929 * A354931 A354932 A354933

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, Jun 14 2022

STATUS

approved

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Last modified February 4 20:58 EST 2023. Contains 360082 sequences. (Running on oeis4.)