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Square array A(n, k) = A009194(A246278(n, k)), read by falling antidiagonals.
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%I #14 Jul 24 2022 10:45:29

%S 1,1,1,6,1,1,1,3,1,1,2,1,1,1,1,4,1,1,1,1,1,2,3,1,1,1,1,1,1,3,1,7,1,1,

%T 1,1,3,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,12,1,

%U 1,7,1,1,1,1,1,1,1,1,2,15,1,7,1,1,1,1,1,1,1,1,1,28,3,1,1,1,1,1,1,1,1,1,1,1,1

%N Square array A(n, k) = A009194(A246278(n, k)), read by falling antidiagonals.

%H Antti Karttunen, <a href="/A355925/b355925.txt">Table of n, a(n) for n = 1..22155; the first 210 antidiagonals</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F A(n, k) = A009194(A246278(n, k)).

%F A(n, k) = gcd(A246278(n,k), A355927(n, k)).

%F A(n, k) = A355927(n, k) / A341605(n, k).

%F A(n, k) = A246278(n, k) / A341606(n, k).

%e The top left corner of the array:

%e k= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

%e 2k= 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42

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

%e 1 | 1, 1, 6, 1, 2, 4, 2, 1, 3, 2, 2, 12, 2, 28, 6, 1, 2, 1, 2, 10, 6,

%e 2 | 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 1, 15, 3, 3, 3, 1, 1, 1, 3, 1, 3,

%e 3 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 7,

%e 4 | 1, 1, 1, 1, 7, 1, 1, 1, 7, 7, 1, 1, 1, 1, 7, 1, 1, 7, 1, 7, 1,

%e 5 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1,

%e 6 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 7 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 8 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 9 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 11 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 31, 1, 1,

%e 12 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1,

%e 16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%e 21 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

%o (PARI)

%o up_to = 105;

%o A009194(n) = gcd(n, sigma(n));

%o 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));

%o A355925sq(row,col) = A009194(A246278sq(row,col));

%o A355925list(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] = A355925sq(col,(a-(col-1))))); (v); };

%o v355925 = A355925list(up_to);

%o A355925(n) = v355925[n];

%Y Cf. A000203, A009194, A246278.

%Y Cf. also A341605, A341606, A341607, A341608, A341626, A341627, A355924, A355927 for related arrays of similar construction.

%K nonn,tabl

%O 1,4

%A _Antti Karttunen_, Jul 22 2022