A355924 Square array A(n,k) = A342671(A246278(n,k)), read by falling antidiagonals, where A342671(x) = gcd(sigma(x), A003961(x)).

3, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 17, 1, 1, 1, 21, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 37, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Jul 21 2022

Keywords

• nonn
• tabl

Examples

			The top left corner of the array:
   n=  1  2  3   4  5  6  7   8  9  10 11  12  13  14 15 16 17 18 19  20 21
  2n=  2  4  6   8 10 12 14  16 18  20 22  24  26  28 30 32 34 36 38  40 42
-----+-----------------------------------------------------------------------
   1 | 3, 1, 3,  3, 3, 1, 3,  1, 3, 21, 3, 15,  3,  1, 3, 9, 3, 1, 3,  9, 3,
   2 | 1, 1, 1,  5, 1, 1, 1,  1, 1,  1, 1,  5,  1, 13, 1, 1, 5, 1, 1,  5, 1,
   3 | 1, 1, 1,  1, 1, 1, 7,  1, 1,  1, 1,  1,  1,  7, 1, 7, 1, 1, 1, 13, 7,
   4 | 1, 1, 1,  1, 1, 1, 1,  1, 1,  1, 1,  1,  1, 19, 1, 1, 1, 1, 1,  1, 1,
   5 | 1, 1, 1,  1, 1, 1, 1,  1, 1, 19, 1,  1,  1,  1, 1, 1, 1, 1, 1,  1, 1,
   6 | 1, 1, 1, 17, 1, 1, 1,  1, 1,  1, 1, 17,  1,  1, 1, 1, 1, 1, 1, 17, 1,
   7 | 1, 1, 1,  1, 1, 1, 1,  1, 1,  1, 1,  1, 19,  1, 1, 1, 1, 1, 1, 29, 1,
   8 | 1, 1, 1,  1, 1, 1, 1,  1, 1,  1, 1,  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, 37, 1, 1, 1,  1, 1,  1, 1, 37,  1,  1, 1, 1, 1, 1, 1, 37, 1,
  12 | 1, 1, 1,  1, 1, 1, 1, 41, 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, 61, 1,  1,  1,  1, 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

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A246278, A342671, A355833.

Cf. also A355925, A355926, A355927 for similarly constructed arrays.

Programs

PARI

up_to = 105;
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));
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A342671(n) = gcd(sigma(n), A003961(n));
A355924sq(row,col) = A342671(A246278sq(row,col));
A355924list(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] = A355924sq(col,(a-(col-1))))); (v); };
v355924 = A355924list(up_to);
A355924(n) = v355924[n];

Formula

A(n,k) = A342671(A246278(n,k)).

A(n, k) = gcd(A246278(1+n,k), A355927(n, k)).