A341607 Square array A(n,k) = A006530(A017666(A246278(n,k))), read by falling antidiagonals.

2, 2, 3, 1, 3, 5, 2, 5, 5, 7, 5, 3, 7, 7, 11, 3, 7, 5, 11, 11, 13, 7, 5, 11, 7, 13, 13, 17, 2, 11, 7, 13, 11, 17, 17, 19, 3, 3, 13, 11, 17, 13, 19, 19, 23, 5, 5, 5, 17, 13, 19, 17, 23, 23, 29, 11, 7, 7, 7, 19, 17, 23, 19, 29, 29, 31, 2, 13, 11, 11, 11, 23, 19, 29, 23, 31, 31, 37, 13, 3, 17, 13, 13, 13, 29, 23, 31, 29, 37, 37, 41

Offset: 1

Author

Antti Karttunen, Feb 16 2021

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
  2n=   2   4   6   8  10  12  14  16  18  20  22  24   26  28  30  32   34
-----+----------------------------------------------------------------------
   1 |  2,  2,  1,  2,  5,  3,  7,  2,  3,  5, 11,  2,  13,  1,  5,  2,  17,
   2 |  3,  3,  5,  3,  7,  5, 11,  3,  5,  7, 13,  3,  17, 11,  7,  3,  19,
   3 |  5,  5,  7,  5, 11,  7, 13,  5,  7, 11, 17,  7,  19, 13, 11,  5,  23,
   4 |  7,  7, 11,  7, 13, 11, 17,  7, 11, 13, 19, 11,  23, 17, 13,  7,  29,
   5 | 11, 11, 13, 11, 17, 13, 19, 11, 13, 17, 23, 13,  29,*11, 17, 11,  31,
   6 | 13, 13, 17, 13, 19, 17, 23, 13, 17, 19, 29,*13,  31, 23, 19, 13,  37,
   7 | 17, 17, 19, 17, 23, 19, 29, 17, 19, 23, 31, 19,  37, 29, 23, 17,  41,
   8 | 19, 19, 23, 19, 29, 23, 31, 19, 23, 29, 37, 23,  41, 31, 29, 19,  43,
   9 | 23, 23, 29, 23, 31, 29, 37, 23, 29, 31, 41, 29,  43, 37, 31, 23,  47,
  10 | 29, 29, 31, 29, 37, 31, 41, 29, 31, 37, 43, 31,  47, 41, 37, 29,  53,
  11 | 31, 31, 37, 31, 41, 37, 43, 31, 37, 41, 47,*31,  53, 43, 41, 31,  59,
  12 | 37, 37, 41, 37, 43, 41, 47, 37, 41, 43, 53, 41,  59, 47, 43, 37,  61,
  13 | 41, 41, 43, 41, 47, 43, 53, 41, 43, 47, 59, 43,  61, 53, 47, 41,  67,
  14 | 43, 43, 47, 43, 53, 47, 59, 43, 47, 53, 61, 47,  67, 59, 53, 43,  71,
  15 | 47, 47, 53, 47, 59, 53, 61, 47, 53, 59, 67, 53,  71, 47, 59, 47,  73,
  16 | 53, 53, 59, 53, 61, 59, 67, 53, 59, 61, 71, 59,  73, 67, 61, 53,  79,
  17 | 59, 59, 61, 59, 67, 61, 71, 59, 61, 67, 73, 61,  79, 71, 67, 59,  83,
  18 | 61, 61, 67, 61, 71, 67, 73, 61, 67, 71, 79, 67,  83, 73, 71, 61,  89,
  19 | 67, 67, 71, 67, 73, 71, 79, 67, 71, 73, 83, 71,  89, 79, 73, 67,  97,
  20 | 71, 71, 73, 71, 79, 73, 83, 71, 73, 79, 89, 73,  97, 83, 79, 71, 101,
  21 | 73, 73, 79, 73, 83, 79, 89, 73, 79, 83, 97, 79, 101, 89, 83, 73, 103,
etc.
Positions where columns are not strictly monotonic are marked with an asterisk (*). See the example section of A341606 for further elaboration.
		

Links

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

Crossrefs

Cf. A006530, A017666, A246278, A341606, A341608, A341628.

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));
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A017666(n) = denominator(sigma(n)/n);
A341607sq(row,col) = A006530(A017666(A246278sq(row,col)));
A341607list(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] = A341607sq(col,(a-(col-1))))); (v); };
v341607 = A341607list(up_to);
A341607(n) = v341607[n];

Formula

A(n,k) = A006530(A341606(n, k)) = A006530(A017666(A246278(n,k))).