A334217 - OEIS

%I #7 Apr 20 2020 09:55:25

%S 1,1,2,1,3,1,2,4,1,5,1,6,1,7,1,2,8,1,3,9,1,10,1,11,1,2,12,1,13,1,14,1,

%T 15,1,2,4,16,1,17,1,3,18,1,19,1,2,20,1,21,1,22,1,23,1,2,24,1,5,25,1,

%U 26,1,3,27,1,2,28,1,29,1,30,1,31,1,2,4,32,1,33

%N Irregular table T(n, k) read by rows, n > 0 and k = 1..A334216(n); n-th row corresponds to distinct terms of n-th row of A334215, in ascending order.

%F T(n, 1) = 1.

%F T(n, 2) = A261969(n) for any n > 1.

%F T(n, A334216(n)-1) = A000188(n) for any n > 1.

%F T(n, A334216(n)) = n.

%e The first rows are:

%e   n     n-th row

%e   --    -------------

%e    1    [1]

%e    2    [1, 2]

%e    3    [1, 3]

%e    4    [1, 2, 4]

%e    5    [1, 5]

%e    6    [1, 6]

%e    7    [1, 7]

%e    8    [1, 2, 8]

%e    9    [1, 3, 9]

%e   10    [1, 10]

%e   11    [1, 11]

%e   12    [1, 2, 12]

%e   13    [1, 13]

%e   14    [1, 14]

%e   15    [1, 15]

%e   16    [1, 2, 4, 16]

%o (PARI) row(n) = { my (f=factor(n)); Set(apply (k -> prod (i=1, #f~, f[i,1]^(f[i,2]\k)), [1..1+if (n==1, 0, vecmax(f[,2]~))])) }

%Y Cf. A000188, A261969, A334215, A334216.

%K nonn,tabf

%O 1,3

%A _Rémy Sigrist_, Apr 19 2020