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%I A355925 #14 Jul 24 2022 10:45:29
%S A355925 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 A355925 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 A355925 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 A355925 Square array A(n, k) = A009194(A246278(n, k)), read by falling antidiagonals.
%H A355925 Antti Karttunen, <a href="/A355925/b355925.txt">Table of n, a(n) for n = 1..22155; the first 210 antidiagonals</a>
%H A355925 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A355925 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A355925 A(n, k) = A009194(A246278(n, k)).
%F A355925 A(n, k) = gcd(A246278(n,k), A355927(n, k)).
%F A355925 A(n, k) = A355927(n, k) / A341605(n, k).
%F A355925 A(n, k) = A246278(n, k) / A341606(n, k).
%e A355925 The top left corner of the array:
%e A355925 k= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%e A355925 2k= 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42
%e A355925 -----+-----------------------------------------------------------------------
%e A355925 1 | 1, 1, 6, 1, 2, 4, 2, 1, 3, 2, 2, 12, 2, 28, 6, 1, 2, 1, 2, 10, 6,
%e A355925 2 | 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 1, 15, 3, 3, 3, 1, 1, 1, 3, 1, 3,
%e A355925 3 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 5, 1, 7,
%e A355925 4 | 1, 1, 1, 1, 7, 1, 1, 1, 7, 7, 1, 1, 1, 1, 7, 1, 1, 7, 1, 7, 1,
%e A355925 5 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1,
%e A355925 6 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 7 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 8 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 9 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 11 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 31, 1, 1,
%e A355925 12 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1,
%e A355925 16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355925 21 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%o A355925 (PARI)
%o A355925 up_to = 105;
%o A355925 A009194(n) = gcd(n, sigma(n));
%o A355925 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 A355925 A355925sq(row,col) = A009194(A246278sq(row,col));
%o A355925 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 A355925 v355925 = A355925list(up_to);
%o A355925 A355925(n) = v355925[n];
%Y A355925 Cf. A000203, A009194, A246278.
%Y A355925 Cf. also A341605, A341606, A341607, A341608, A341626, A341627, A355924, A355927 for related arrays of similar construction.
%K A355925 nonn,tabl
%O A355925 1,4
%A A355925 _Antti Karttunen_, Jul 22 2022