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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)]. 5

%I

%S 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,

%T 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,

%U 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

%N 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)].

%C 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.

%H Antti Karttunen, <a href="/A320000/b320000.txt">Table of n, a(n) for n = 1..10585; the first 145 antidiagonals of the array</a>

%e Array begins as:

%e n | k=1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16, ...

%e ---+------------------------------------------------

%e 1 | 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%e 2 | 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 3 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 4 | 4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 5 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 6 | 4, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 7 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 8 | 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 9 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 10 | 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, ...

%e 11 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 12 | 6, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, ...

%e 13 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 14 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 15 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 16 | 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...

%o (PARI)

%o up_to = 120;

%o 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

%o 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); };

%o v320000 = A320000list(up_to);

%o A320000(n) = v320000[n];

%Y Cf. A014197 (column 1).

%Y Cf. A000010, A322310.

%K nonn,tabl

%O 1,1

%A _Antti Karttunen_, Dec 03 2018

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)