A337470 - OEIS

%I #10 Aug 28 2020 11:07:10

%S 1,2,1,6,3,1,4,15,5,1,30,9,35,7,1,12,105,25,77,11,1,210,45,385,49,143,

%T 13,1,8,1155,175,1001,121,221,17,1,36,27,5005,539,2431,169,323,19,1,

%U 60,225,125,17017,1573,4199,289,437,23,1,2310,315,1225,343,46189,2873,7429,361,667,29,1,24,15015,1925,5929,1331,96577,5491,12673,529,899,31

%N Square array read by falling antidiagonals, where A(n,k) = primorial inflation of k prime shifted n times with A003961.

%C Array is read by descending antidiagonals with n >= 0 and k >= 1 ranging as: (0, 1), (0, 2), (1, 1), (0, 3), (1, 2), (2, 1), (0, 4), (1, 3), (2, 2), (3, 1), ...

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

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F A(n,k) = A242378(n,A108951(k)).

%e The top left corner of the array begins as:

%e n/k | 1   2    3    4     5     6      7     8      9     10

%e ----|------------------------------------------------------------

%e   0 | 1,  2,   6,   4,   30,   12,   210,    8,    36,    60, ...

%e   1 | 1,  3,  15,   9,  105,   45,  1155,   27,   225,   315, ...

%e   2 | 1,  5,  35,  25,  385,  175,  5005,  125,  1225,  1925, ...

%e   3 | 1,  7,  77,  49, 1001,  539, 17017,  343,  5929,  7007, ...

%e   4 | 1, 11, 143, 121, 2431, 1573, 46189, 1331, 20449, 26741, ...

%e   5 | 1, 13, 221, 169, 4199, 2873, 96577, 2197, 48841, 54587, ...

%e etc.

%o (PARI)

%o up_to = 105-1; \\ Or 78-1.

%o Ashifted_primorial(n,d) = prod(i=1, primepi(n), prime(i+d));

%o A337470sq(n, k) = { my(f=factor(k)); prod(i=1, #f~, Ashifted_primorial(f[i, 1], n)^f[i, 2]); };

%o A337470list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(b=1, a, i++; if(i > #v, return(v)); v[i] = A337470sq(b-1, (a-(b-1))))); (v); };

%o v337470 = A337470list(up_to);

%o A337470(n) = v337470[1+n];

%Y Cf. A108951 (row 0), A337471 (row 1).

%Y Cf. A003961, A242378.

%Y Cf. also A337205, A337472.

%K nonn,tabl

%O 0,2

%A _Antti Karttunen_, Aug 28 2020