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

1,1

Links

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

Formula

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

Example

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,

Prog

(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];

Crossrefs

Cf. A006530, A246278, A341527, A341627.

Cf. also A341607.

Sequence in context: A021731 A084726 A107738 * A238048 A010624 A019638

Adjacent sequences: A341625 A341626 A341627 * A341629 A341630 A341631

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 16 2021

Status

approved