cp's OEIS Frontend

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.

%I A273673 #24 Jun 24 2017 05:38:05
%S A273673 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,
%T A273673 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,
%U A273673 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
%N 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.
%C A273673 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.
%C A273673 Auxiliary function for computing array A275723.
%H A273673 Antti Karttunen, <a href="/A273673/b273673.txt">Table of n, a(n) for n = 1..5050; the first 100 antidiagonals of array</a>
%H A273673 Indranil Ghosh, <a href="/A273673/a273673.txt">Python program for computing this sequence</a>
%H A273673 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A273673 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.
%e A273673 The top left 6 x 15 corner of the array:
%e A273673    1,  1,  1,  1,  1,  1
%e A273673    2,  2,  2,  2,  2,  2
%e A273673    2,  3,  3,  3,  3,  3
%e A273673    4,  4,  4,  4,  4,  4
%e A273673    5,  3,  3,  2,  2,  5
%e A273673    4,  6,  6,  6,  6,  6
%e A273673    7,  7,  7,  7,  7,  5
%e A273673    8,  8,  8,  8,  8,  8
%e A273673    4,  9,  9,  9,  9,  9
%e A273673   10,  6,  6,  4,  4, 10
%e A273673   11, 11, 11, 11, 11, 11
%e A273673    8, 12, 12, 12, 12, 12
%e A273673   13, 13, 13, 13, 13, 13
%e A273673   14, 14, 14, 14, 14, 10
%e A273673   10,  9,  9,  6,  6, 15
%o A273673 (Scheme)
%o A273673 (define (A273673 n) (A273673bi (A002260 n) (A004736 n)))
%o A273673 (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)))))
%o A273673 ;; Code for A249344bi given in A249344.
%Y A273673 Cf. A000040, A084558, A099563, A249344.
%Y A273673 Cf. also A007623, A275723.
%K A273673 nonn,base,tabl
%O A273673 1,3
%A A273673 _Antti Karttunen_, Aug 09 2016