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

0,2

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), ...

Links

Table of n, a(n) for n=0..76.

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to primorial numbers

Formula

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

Example

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.

Prog

(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];

Crossrefs

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

Cf. A003961, A242378.

Cf. also A337205, A337472.

Sequence in context: A284431 A333078 A352376 * A006019 A201146 A065553

Adjacent sequences: A337467 A337468 A337469 * A337471 A337472 A337473

Keyword

nonn,tabl

Author

Antti Karttunen, Aug 28 2020

Status

approved