A337472 Square array read by falling antidiagonals, where A(n,k) = sigma(A337470(n, k)).

1, 3, 1, 12, 4, 1, 7, 24, 6, 1, 72, 13, 48, 8, 1, 28, 192, 31, 96, 12, 1, 576, 78, 576, 57, 168, 14, 1, 15, 2304, 248, 1344, 133, 252, 18, 1, 91, 40, 8064, 684, 3024, 183, 360, 20, 1, 168, 403, 156, 24192, 1862, 5040, 307, 480, 24, 1, 6912, 624, 1767, 400, 60480, 3294, 8640, 381, 720, 30, 1

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,  3,  12,   7,   72,   28,    576,   15,    91,   168, ...
  1 | 1,  4,  24,  13,  192,   78,   2304,   40,   403,   624, ...
  2 | 1,  6,  48,  31,  576,  248,   8064,  156,  1767,  2976, ...
  3 | 1,  8,  96,  57, 1344,  684,  24192,  400,  7581,  9576, ...
  4 | 1, 12, 168, 133, 3024, 1862,  60480, 1464, 24339, 33516, ...
  5 | 1, 14, 252, 183, 5040, 3294, 120960, 2380, 56181, 65880, ...
etc.
		

Links

• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial numbers
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961.

Cf. A337203 (row 0).

Cf. also arrays A337205, A337470.

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]); };
A337472sq(n, k) = sigma(A337470sq(n, k));
A337472list(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] = A337472sq(b-1, (a-(b-1))))); (v); };
v337472 = A337472list(up_to);
A337472(n) = v337472[1+n];

Formula

A(n,k) = A000203(A337470(n, k)).