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A273673
Square array A(n,k) = (n / prime(1+A084558(k))^e) * prime(1+A084558(k)-A099563(k))^e, where e = A249344((1+A084558(k)), n) = the exponent of the largest power of prime(1+A084558(k)) which divides n. Array is read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
2
1, 1, 2, 1, 2, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 3, 4, 1, 2, 3, 4, 3, 6, 7, 1, 2, 3, 4, 2, 6, 7, 8, 1, 2, 3, 4, 2, 6, 7, 8, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 11, 1, 2, 3, 4, 5, 6, 5, 8, 9, 6, 11, 8, 1, 2, 3, 4, 5, 6, 5, 8, 9, 4, 11, 12, 13, 1, 2, 3, 4, 5, 6, 5, 8, 9, 4, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 5, 8, 9, 10, 11, 12, 13, 14, 10
OFFSET
1,3
COMMENTS
Informally: "clear" the exponent of prime(1+A084558(k)) and add it (the old value of exponent) to the exponent of prime(1+A084558(k)-A099563(k)) in the prime factorization of n.
Auxiliary function for computing array A275723.
FORMULA
A(n,k) = (n / prime(1+A084558(k))^e) * prime(1+A084558(k)-A099563(k))^e, where e = A249344((1+A084558(k)), n), the exponent of the largest power prime(1+A084558(k)) which divides n.
EXAMPLE
The top left 6 x 15 corner of the array:
1, 1, 1, 1, 1, 1
2, 2, 2, 2, 2, 2
2, 3, 3, 3, 3, 3
4, 4, 4, 4, 4, 4
5, 3, 3, 2, 2, 5
4, 6, 6, 6, 6, 6
7, 7, 7, 7, 7, 5
8, 8, 8, 8, 8, 8
4, 9, 9, 9, 9, 9
10, 6, 6, 4, 4, 10
11, 11, 11, 11, 11, 11
8, 12, 12, 12, 12, 12
13, 13, 13, 13, 13, 13
14, 14, 14, 14, 14, 10
10, 9, 9, 6, 6, 15
PROG
(Scheme)
(define (A273673 n) (A273673bi (A002260 n) (A004736 n)))
(define (A273673bi n c) (if (zero? c) n (* (/ n (expt (A000040 (+ 1 (A084558 c))) (A249344bi (+ 1 (A084558 c)) n))) (expt (A000040 (+ 1 (- (A084558 c) (A099563 c)))) (A249344bi (+ 1 (A084558 c)) n)))))
;; Code for A249344bi given in A249344.
CROSSREFS
KEYWORD
nonn,base,tabl
AUTHOR
Antti Karttunen, Aug 09 2016
STATUS
approved