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

1,1

Links

Table of n, a(n) for n=1..91.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

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

Prog

(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];

Crossrefs

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

Sequence in context: A257522 A059897 A325821 * A303719 A299595 A304270

Adjacent sequences: A341604 A341605 A341606 * A341608 A341609 A341610

Keyword

nonn,tabl

Author

Antti Karttunen, Feb 16 2021

Status

approved