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%I A355924 #9 Jul 22 2022 10:37:50
%S A355924 3,1,1,3,1,1,3,1,1,1,3,5,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,1,
%T A355924 1,1,3,1,7,1,1,17,1,1,1,21,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,15,
%U A355924 1,1,1,1,1,1,1,1,1,1,1,3,5,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,19,1,1,1,1,1,37,1,1,1
%N A355924 Square array A(n,k) = A342671(A246278(n,k)), read by falling antidiagonals, where A342671(x) = gcd(sigma(x), A003961(x)).
%H A355924 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A355924 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A355924 A(n,k) = A342671(A246278(n,k)).
%F A355924 A(n, k) = gcd(A246278(1+n,k), A355927(n, k)).
%e A355924 The top left corner of the array:
%e A355924 n= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%e A355924 2n= 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42
%e A355924 -----+-----------------------------------------------------------------------
%e A355924 1 | 3, 1, 3, 3, 3, 1, 3, 1, 3, 21, 3, 15, 3, 1, 3, 9, 3, 1, 3, 9, 3,
%e A355924 2 | 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1, 13, 1, 1, 5, 1, 1, 5, 1,
%e A355924 3 | 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 7, 1, 7, 1, 1, 1, 13, 7,
%e A355924 4 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1,
%e A355924 5 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 6 | 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 17, 1,
%e A355924 7 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 29, 1,
%e A355924 8 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 9 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 11 | 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 1, 37, 1, 1, 1, 1, 1, 1, 1, 37, 1,
%e A355924 12 | 1, 1, 1, 1, 1, 1, 1, 41, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 61, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%e A355924 21 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
%o A355924 (PARI)
%o A355924 up_to = 105;
%o A355924 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 A355924 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A355924 A342671(n) = gcd(sigma(n), A003961(n));
%o A355924 A355924sq(row,col) = A342671(A246278sq(row,col));
%o A355924 A355924list(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] = A355924sq(col,(a-(col-1))))); (v); };
%o A355924 v355924 = A355924list(up_to);
%o A355924 A355924(n) = v355924[n];
%Y A355924 Cf. A000203, A003961, A246278, A342671, A355833.
%Y A355924 Cf. also A355925, A355926, A355927 for similarly constructed arrays.
%K A355924 nonn,tabl
%O A355924 1,1
%A A355924 _Antti Karttunen_, Jul 21 2022