A337470 Square array read by falling antidiagonals, where A(n,k) = primorial inflation of k prime shifted n times with A003961.

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

Offset: 0

Author

Antti Karttunen, Aug 28 2020

Keywords

• nonn
• tabl

Comments

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), ...

Examples

			The top left corner of the array begins as:
n/k | 1   2    3    4     5     6      7     8      9     10
----|------------------------------------------------------------
  0 | 1,  2,   6,   4,   30,   12,   210,    8,    36,    60, ...
  1 | 1,  3,  15,   9,  105,   45,  1155,   27,   225,   315, ...
  2 | 1,  5,  35,  25,  385,  175,  5005,  125,  1225,  1925, ...
  3 | 1,  7,  77,  49, 1001,  539, 17017,  343,  5929,  7007, ...
  4 | 1, 11, 143, 121, 2431, 1573, 46189, 1331, 20449, 26741, ...
  5 | 1, 13, 221, 169, 4199, 2873, 96577, 2197, 48841, 54587, ...
etc.
		

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers

Crossrefs

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

Cf. A003961, A242378.

Cf. also A337205, A337472.

Programs

PARI

up_to = 105-1; \\ Or 78-1.
Ashifted_primorial(n,d) = prod(i=1, primepi(n), prime(i+d));
A337470sq(n, k) = { my(f=factor(k)); prod(i=1, #f~, Ashifted_primorial(f[i, 1], n)^f[i, 2]); };
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); };
v337470 = A337470list(up_to);
A337470(n) = v337470[1+n];

Formula

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