A320000 Square array A(n, k) read by descending antidiagonals: A(1, 1) = 2, A(1, k) = 1 for k > 1, and for n > 1, A(n, k) = Sum_{d|n, d>=k} A010051(1+d)*[Sum_{i=0..valuation(n,1+d)} A((n/d)/((1+d)^i), 1+d)].

2, 1, 3, 1, 1, 0, 1, 0, 0, 4, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 4, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 0, 5, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0

Offset

1,1

Comments

This square array gives the values obtained from the recursive PARI-program that M. F. Hasler has provided Oct 05 2009 for A014197, in its two-argument form.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of the array

Example

Array begins as:
n  | k=1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16, ...
---+------------------------------------------------
1  |   2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2  |   3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
3  |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
4  |   4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
5  |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
6  |   4, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
7  |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
8  |   5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
9  |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
10 |   2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...
11 |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
12 |   6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, ...
13 |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
14 |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
15 |   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
16 |   6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

Prog

(PARI)
up_to = 120;
A320000sq(n, k) = if(1==n, if(1==k, 2, 1), sumdiv(n, d, if(d>=k && isprime(d+1), my(p=d+1, q=n/d); sum(i=0, valuation(n, p), A320000sq(q/(p^i), p))))); \\ After M. F. Hasler's code in A014197
A320000list(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] = A320000sq(col, (a-(col-1))))); (v); };
v320000 = A320000list(up_to);
A320000(n) = v320000[n];

Crossrefs

Cf. A014197 (column 1).

Cf. A000010, A322310.

Sequence in context: A376682 A350004 A144966 * A119805 A111957 A125168

Adjacent sequences: A319997 A319998 A319999 * A320001 A320002 A320003

Keyword

nonn,tabl

Author

Antti Karttunen, Dec 03 2018

Status

approved