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A342674
Square array A(n,k) = A341530(A246278(n,k)), read by falling antidiagonals; A341530 as applied onto prime shift array A246278.
3
1, 1, 2, 36, 1, 2, 5, 120, 1, 4, 2, 4, 336, 19, 2, 36, 8, 4, 264, 1, 2, 24, 30, 56, 8, 1092, 1, 2, 1, 12, 28, 56, 4, 612, 1, 4, 9, 11, 12, 418, 8, 20, 2280, 1, 6, 2, 10, 1, 48, 26, 8, 20, 5520, 1, 2, 4, 4, 266, 1, 48, 34, 24, 40, 6960, 1, 2, 180, 4, 42, 308, 1, 12, 76, 24, 60, 1984, 3, 2, 18, 240, 4, 798, 26, 1, 20, 138, 12, 4, 2812, 1, 2
OFFSET
1,3
FORMULA
A(n,k) = A341530(A246278(n,k)).
EXAMPLE
The top left corner of the array:
k = 1 2 3 4 5 6 7 8 9 10 11 12 13 14
2k = 2 4 6 8 10 12 14 16 18 20 22 24 26 28
|
-----+--------------------------------------------------------------------------
n= 1 | 1, 1, 36, 5, 2, 36, 24, 1, 9, 2, 4, 180, 18, 168,
2 | 2, 1, 120, 4, 8, 30, 12, 11, 10, 4, 4, 240, 360, 6,
3 | 2, 1, 336, 4, 56, 28, 12, 1, 266, 42, 4, 672, 120, 2,
4 | 4, 19, 264, 8, 56, 418, 48, 1, 308, 798, 32, 528, 24, 38,
5 | 2, 1, 1092, 4, 8, 26, 48, 1, 26, 6, 12, 37128, 8, 76,
6 | 2, 1, 612, 20, 8, 34, 12, 1, 34, 12, 12, 6120, 4, 6,
7 | 2, 1, 2280, 20, 24, 76, 20, 1, 38, 6, 152, 4560, 12, 6,
8 | 4, 1, 5520, 40, 24, 138, 16, 1, 92, 2, 152, 11040, 24, 2,
9 | 6, 1, 6960, 60, 12, 58, 12, 1, 174, 2, 24, 13920, 96, 14,
10 | 2, 1, 1984, 4, 12, 62, 4, 1, 186, 2, 24, 146816, 288, 6,
11 | 2, 3, 2812, 4, 8, 222, 32, 11, 74, 42, 12, 5624, 24, 12,
12 | 2, 1, 3444, 4, 8, 82, 12, 1, 82, 12, 36, 6888, 12, 18,
PROG
(PARI)
up_to = 91;
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
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));
A342674sq(row, col) = A341530(A246278sq(row, col));
A342674list(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] = A342674sq(col, (a-(col-1))))); (v); };
v342674 = A342674list(up_to);
A342674(n) = v342674[n];
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Mar 24 2021
STATUS
approved