A355925 Square array A(n, k) = A009194(A246278(n, k)), read by falling antidiagonals.

1, 1, 1, 6, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 2, 15, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 28, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Jul 22 2022

Keywords

• nonn
• tabl

Examples

			The top left corner of the array:
   k=  1  2  3  4  5  6  7  8  9 10  11  12 13  14 15 16 17 18  19  20 21
  2k=  2  4  6  8 10 12 14 16 18 20  22  24 26  28 30 32 34 36  38  40 42
-----+-----------------------------------------------------------------------
   1 | 1, 1, 6, 1, 2, 4, 2, 1, 3, 2,  2, 12, 2, 28, 6, 1, 2, 1,  2, 10, 6,
   2 | 1, 1, 3, 1, 1, 3, 3, 1, 1, 1,  1, 15, 3,  3, 3, 1, 1, 1,  3,  1, 3,
   3 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 5,  1, 1, 1, 1, 1,  5,  1, 7,
   4 | 1, 1, 1, 1, 7, 1, 1, 1, 7, 7,  1,  1, 1,  1, 7, 1, 1, 7,  1,  7, 1,
   5 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1, 19, 1, 1, 1, 1,  1,  1, 1,
   6 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 17, 1,  1, 1, 1, 1, 1,  1,  1, 1,
   7 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
   8 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
   9 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  11 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1, 37, 1,  1, 1, 1, 1, 1, 31,  1, 1,
  12 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1, 61, 1, 1, 1, 1,  1,  1, 1,
  16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
  21 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,  1,  1, 1,  1, 1, 1, 1, 1,  1,  1, 1,
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A009194, A246278.

Cf. also A341605, A341606, A341607, A341608, A341626, A341627, A355924, A355927 for related arrays of similar construction.

Programs

PARI

up_to = 105;
A009194(n) = gcd(n, sigma(n));
A246278sq(row,col) = if(1==row,2*col, my(f = factor(2*col)); for(i=1, #f~, f[i,1] = prime(primepi(f[i,1])+(row-1))); factorback(f));
A355925sq(row,col) = A009194(A246278sq(row,col));
A355925list(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] = A355925sq(col,(a-(col-1))))); (v); };
v355925 = A355925list(up_to);
A355925(n) = v355925[n];

Formula

A(n, k) = A009194(A246278(n, k)).

A(n, k) = gcd(A246278(n,k), A355927(n, k)).

A(n, k) = A355927(n, k) / A341605(n, k).

A(n, k) = A246278(n, k) / A341606(n, k).