A355926 - OEIS

%I #4 Jul 22 2022 10:37:59

%S 3,9,1,5,5,1,3,5,1,1,3,125,7,1,1,5,5,343,1,1,1,3,175,7,11,1,1,1,9,1,

%T 49,1,1,1,1,1,25,125,7,121,1,1,1,1,1,3,245,2401,1,1,1,1,1,1,1,3,1,77,

%U 1,1,1,1,1,1,1,1,5,5,49,11,28561,1,1,1,1,1,1,1,3,175,7,121,1,1,1,1,1,1,1,1,1,9,5,77,1,1,1,1,1,1,1,1,1,1,1

%N Square array A(n,k) = A355442(A246278(n,k)), read by falling antidiagonals.

%e The top left corner of the array:

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

%e   2n= 2  4  6    8 10   12 14     16   18   20 22     24 26   28  30       32

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

%e   1 | 3, 9, 5,   3, 3,   5, 3,     9,  25,   3, 3,     5, 3,   9,  7,       3,

%e   2 | 1, 5, 5, 125, 5, 175, 1,   125, 245,   1, 5,   175, 5,   5, 35,       1,

%e   3 | 1, 1, 7, 343, 7,  49, 7,  2401,  77,  49, 7,    77, 7,  49, 77,   16807,

%e   4 | 1, 1, 1,  11, 1, 121, 1,     1,  11, 121, 1, 17303, 1, 121, 11,    1331,

%e   5 | 1, 1, 1,   1, 1,   1, 1, 28561,   1,   1, 1,  2197, 1,   1, 13,   28561,

%e   6 | 1, 1, 1,   1, 1,   1, 1,     1,   1,   1, 1,    17, 1,   1,  1, 1419857,

%e   7 | 1, 1, 1,   1, 1,   1, 1,     1,   1,   1, 1,     1, 1,   1,  1,     361,

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

%o (PARI)

%o up_to = 105;

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A355442(n) = gcd(A003961(n), A276086(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 A355926sq(row,col) = A355442(A246278sq(row,col));

%o A355926list(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] = A355926sq(col,(a-(col-1))))); (v); };

%o v355926 = A355926list(up_to);

%o A355926(n) = v355926[n];

%Y Cf. A003961, A246278, A276086, A355442, A355835.

%Y Cf. also A355924, A355925 for similarly constructed arrays.

%K nonn,tabl

%O 1,1

%A _Antti Karttunen_, Jul 22 2022