cp's OEIS Frontend

A104245 Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then we can define Pn(x) = e1 + (e2)*x + (e3)*(x^2) + (e4)*(x^3) + ... + (ek)*(x^(k-1)) + ... The sequence is the table T(x,n)=Pn(x) read by antidiagonals.

%I A104245 #11 Aug 02 2015 17:51:46
%S A104245 0,0,1,0,1,1,0,1,2,2,0,1,3,2,1,0,1,4,2,4,2,0,1,5,2,9,3,1,0,1,6,2,16,4,
%T A104245 8,3,0,1,7,2,25,5,27,3,2,0,1,8,2,36,6,64,3,4,2,0,1,9,2,49,7,125,3,6,5,
%U A104245 1,0,1,10,2,64,8,216,3,8,10,16,3,0,1,11,2,81,9,343,3,10,17,81,4,1,0,1,12,2
%N A104245 Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then we can define Pn(x) = e1 + (e2)*x + (e3)*(x^2) + (e4)*(x^3) + ... + (ek)*(x^(k-1)) + ... The sequence is the table T(x,n)=Pn(x) read by antidiagonals.
%C A104245 This square array is the transpose of A104244, see comments there.
%e A104245 a(13)=3 because 3=(p1^0)(p2^1)(p3^0)..., so P3(x)=x. Hence a(13) = T(3,3) = P3(3) = 3.
%e A104245 The top left corner of the array:
%e A104245 0,  0,  0,   0,   0,    0,    0,    0,    0,    0,      0,     0
%e A104245 1,  1,  1,   1,   1,    1,    1,    1,    1,    1,      1,     1
%e A104245 1,  2,  3,   4,   5,    6,    7,    8,    9,   10,     11,    12
%e A104245 2,  2,  2,   2,   2,    2,    2,    2,    2,    2,      2,     2
%e A104245 1,  4,  9,  16,  25,   36,   49,   64,   81,  100,    121,   144
%e A104245 2,  3,  4,   5,   6,    7,    8,    9,   10,   11,     12,    13
%e A104245 1,  8, 27,  64, 125,  216,  343,  512,  729, 1000,   1331,  1728
%e A104245 3,  3,  3,   3,   3,    3,    3,    3,    3,    3,      3,     3
%e A104245 2,  4,  6,   8,  10,   12,   14,   16,   18,   20,     22,    24
%e A104245 2,  5, 10,  17,  26,   37,   50,   65,   82,   101,   122,   145
%e A104245 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000, 14641, 20736
%e A104245 3,  4,  5,   6,   7,    8,    9,   10,   11,    12,    13,    14
%e A104245 ...
%o A104245 (Scheme)
%o A104245 (define (A104245 n) (A104244bi (A004736 n) (A002260 n))) ;; A104244bi given in A104244.
%o A104245 ;; _Antti Karttunen_, Jul 29 2015
%Y A104245 Transpose: A104244.
%Y A104245 Main diagonal: A090883.
%K A104245 easy,nonn,tabl
%O A104245 1,9
%A A104245 _Olaf Voß_, Feb 26 2005
%E A104245 Starting offset changed from 0 to 1 by _Antti Karttunen_, Jul 29 2015