A341628 Square array A(n,k) = A006530(A341527(A246278(n,k))), read by falling antidiagonals.

3, 7, 5, 5, 13, 7, 3, 7, 31, 11, 7, 5, 11, 11, 13, 7, 11, 13, 13, 19, 17, 11, 13, 13, 11, 17, 61, 19, 31, 13, 31, 17, 61, 19, 307, 23, 13, 11, 17, 13, 19, 17, 23, 127, 29, 7, 31, 71, 19, 19, 23, 29, 29, 79, 31, 13, 13, 11, 2801, 23, 61, 29, 181, 31, 67, 37, 5, 17, 31, 19, 3221, 29, 307, 31, 53, 37, 331, 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
  2n=   2     4   6     8  10    12  14       16    18    20  22    24  26    28
-----+---------------------------------------------------------------------------
   1 |  3,    7,  5,    3,  7,    7, 11,      31,   13,    7, 13,    5, 17,   11,
   2 |  5,   13,  7,    5, 11,   13, 13,      11,   31,   13, 17,    7, 19,   13,
   3 |  7,   31, 11,   13, 13,   31, 17,      71,   11,   31, 19,   13, 23,   31,
   4 | 11,   11, 13,   11, 17,   13, 19,    2801,   19,   17, 23,   13, 29,   19,
   5 | 13,   19, 17,   61, 19,   19, 23,    3221,   61,   19, 29,   61, 31,   23,
   6 | 17,   61, 19,   17, 23,   61, 29,   30941,  307,   61, 31,   19, 37,   61,
   7 | 19,  307, 23,   29, 29,  307, 31,   88741,  127,  307, 37,   29, 41,  307,
   8 | 23,  127, 29,  181, 31,  127, 37,     911,   79,  127, 41,  181, 43,  127,
   9 | 29,   79, 31,   53, 37,   79, 41,  292561,   67,   79, 43,   53, 47,   79,
  10 | 31,   67, 37,  421, 41,   67, 43,  732541,  331,   67, 47,  421, 53,   67,
  11 | 37,  331, 41,   37, 43,  331, 47,   17351,   67,  331, 53,   41, 59,  331,
  12 | 41,   67, 43,  137, 47,   67, 53,    4271, 1723,   67, 59,  137, 61,   67,
  13 | 43, 1723, 47,   43, 53, 1723, 59,  579281,  631, 1723, 61,   47, 67, 1723,
  14 | 47,  631, 53,   47, 59,  631, 61, 3500201,   61,  631, 67,   53, 71,  631,
  15 | 53,   61, 59,   53, 61,   61, 67,   14621,  409,   61, 71,   59, 73,   67,
  16 | 59,  409, 61,  281, 67,  409, 71,    5581, 3541,  409, 73,  281, 79,  409,
  17 | 61, 3541, 67, 1741, 71, 3541, 73,     181,   97, 3541, 79, 1741, 83, 3541,
  18 | 67,   97, 71, 1861, 73,   97, 79,   21491,   71,   97, 83, 1861, 89,   97,
  19 | 71,   71, 73,  449, 79,   73, 83,   26881, 5113,   79, 89,  449, 97,   83,
		

Crossrefs

Cf. A006530, A246278, A341527, A341627.

Cf. also A341607.

Programs

PARI

up_to = 105;
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A341528(n) = (n*sigma(A003961(n)));
A341529(n) = (sigma(n)*A003961(n));
A341527(n) = denominator(A341528(n) / A341529(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));
A341628sq(row,col) = A006530(A341527(A246278sq(row,col)));
A341628list(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] = A341628sq(col,(a-(col-1))))); (v); };
v341628 = A341628list(up_to);
A341628(n) = v341628[n];

Formula

A(n,k) = A006530(A341627(n,k)) = A006530(A341527(A246278(n,k))).