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A060176
Square array A(n,k) = the largest power of k-th prime which divides n, read by falling antidiagonals.
3
1, 1, 2, 1, 1, 1, 1, 1, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 9, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2
OFFSET
1,3
COMMENTS
Product of terms on row n is n.
FORMULA
A(n, k) = A000040(k)^A060175(n, k).
EXAMPLE
The top left corner of the array:
n\k | 1 2 3 4 5 6 7 8
----+---------------------------------
1 | 1, 1, 1, 1, 1, 1, 1, 1,
2 | 2, 1, 1, 1, 1, 1, 1, 1,
3 | 1, 3, 1, 1, 1, 1, 1, 1,
4 | 4, 1, 1, 1, 1, 1, 1, 1,
5 | 1, 1, 5, 1, 1, 1, 1, 1,
6 | 2, 3, 1, 1, 1, 1, 1, 1,
7 | 1, 1, 1, 7, 1, 1, 1, 1,
8 | 8, 1, 1, 1, 1, 1, 1, 1,
9 | 1, 9, 1, 1, 1, 1, 1, 1,
10 | 2, 1, 5, 1, 1, 1, 1, 1,
11 | 1, 1, 1, 1, 11, 1, 1, 1,
12 | 4, 3, 1, 1, 1, 1, 1, 1,
13 | 1, 1, 1, 1, 1, 13, 1, 1,
14 | 2, 1, 1, 7, 1, 1, 1, 1,
15 | 1, 3, 5, 1, 1, 1, 1, 1,
16 | 16, 1, 1, 1, 1, 1, 1, 1,
17 | 1, 1, 1, 1, 1, 1, 17, 1,
18 | 2, 9, 1, 1, 1, 1, 1, 1,
19 | 1, 1, 1, 1, 1, 1, 1, 19,
...
a(12,1) = 4 since 4 = 2^2 = prime(1)^2 divides 12 but 8 = 2^3 does not.
PROG
(PARI)
up_to = 105;
A060176sq(n, k) = (prime(k)^valuation(n, prime(k)));
A060176list(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] = A060176sq(col, (a-(col-1))))); (v); };
v060176 = A060176list(up_to);
A060176(n) = v060176[n]; \\ Antti Karttunen, Jan 16 2025
CROSSREFS
Columns include A006519, A038500.
Sequence in context: A361754 A298848 A193518 * A305297 A218220 A247487
KEYWORD
easy,nonn,tabl
AUTHOR
Henry Bottomley, Mar 14 2001
EXTENSIONS
Edited by Antti Karttunen, Jan 16 2025
STATUS
approved